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In the fields of oceanography, hydrodynamics, and marine engineering, many mathematicians and physicists are interested in Burgers-type equations to show the different dynamics of nonlinear wave phenomena, one of which is a (3+1)-dimensional Burgers system that is currently being studied. In this paper, we apply two different analytical methods, namely the generalized Kudryashov (GK) method, and the generalized exponential rational function method, to derive abundant novel analytic exact solitary wave solutions, including multi-wave solitons, multi-wave peakon solitons, kink-wave profiles, stripe solitons, wave-wave interaction profiles, and periodic oscillating wave profiles for a (3+1)-dimensional Burgers system with the assistance of symbolic computation. By employing the generalized Kudryashov method, we obtain some new families of exact solitary wave solutions for the Burgers system. Further, we applied the generalized exponential rational function method to obtain a large number of soliton solutions in the forms of trigonometric and hyperbolic function solutions, exponential rational function solutions, periodic breather-wave soliton solutions, dark and bright solitons, singular periodic oscillating wave soliton solutions, and complex multi-wave solutions under various family cases. Based on soft computing via Wolfram Mathematica, all the newly established solutions are verified by back substituting them into the considered Burgers system. Eventually, the dynamical behaviors of some established results are exhibited graphically through three - and two-dimensional wave profiles via numerical simulation.

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed.

In this work, the head-on collisions of the non-stationary dissipative soliton in ultracold neutral plasmas (UNPs) are investigated. The extended Poincare-Lighthill-Kuo (PLK) approach is adopted for reducing the fluid equations of the UNPs to two-counterpropagating damped Korteweg-de Vries (dKdV) equations. The dKdV equation is not an integrable Hamiltonian system, i.e., does not have an exact solution. Thus, one of the main goal of this paper is to find a new general approximate analytical solution to the dKdV equation for investigating the mechanism of the propagation and interaction of the non-stationary dissipative solitons. The residual error is estimated for checking the accuracy of the new obtained solution. The approximate analytical soliton solutions are adopted for deriving the temporal phase shifts after the collision. The impact of physical parameters on the nonstationary dissipative soliton profile and the temporal phase shifts is discussed. The obtained results will contribute to understand the mechanism of propagation and interaction of many nonlinear phenomena in different nonlinear mediums such as ocean, sea, optical fiber, plasma physics, etc.

Fractional order nonlinear evolution equations have emerged in recent times as being very important model for depicting the interior behavior of nonlinear phenomena that exist in the real world. In particular, Schrodinger-type fractional nonlinear evolution equations constitute an aspect of the field of quantum mechanics. In this study, the (2 + 1)-dimensional time-fractional nonlinear Schrodinger equation and (1 + 1)-dimensional time-space fractional nonlinear Schrodinger equation are revealed as having different and novel wave structures. This is shown by constructing appropriate analytic wave solutions. A successful implementation of the advised rational ( 1 / ϕ ′ ( ξ ) ) -expansion method generates new outcomes of the considered equations, by comparing them with those already noted in the literature. On the basis of the conformable fractional derivative, a composite wave variable conversion has been used to adapt the suggested equations into the differential equations with a single independent variable before applying the scheme. Finally, the well-furnished outcomes are plotted in different 3D and 2D profiles for the purpose of illustrating various physical characteristics of wave structures. The employed technique is competent, productive and concise enough, making it feasible for future studies.

Most finite element models of small arms focus on an idealized barrel, typically one with a perfectly straight bore centerline. Using five different experimentally measured bore centerlines, this investigation analyzes the effect centerline nonlinearity has on projectile exit conditions. This includes the effect of rotating a centerline through several orientations. Modeled using Abaqus/Explicit, this dynamic analysis simulates a single firing cycle for each centerline. Projectile jump is calculated for each model as a measure of the effects of warped centerlines. The warped centerlines have a small effect on barrel dynamics.

In this paper we study integral-input-to-state stability (iISS) of nonlinear switched systems with jumps. We demonstrate by examples that iISS is not always preserved under slow enough dwell time switching, and then we present sufficient conditions for iISS to be preserved under slow switching. These conditions involve, besides a sufficiently large dwell time, some additional properties of comparison functions characterizing iISS of the individual modes. When the sufficient conditions that guarantee iISS are only partially satisfied, we are then able to conclude weaker variants of iISS, also introduced in this work. As an illustration, we show that switched systems with bilinear zero-input-stable modes are always iISS under sufficiently large dwell time.

In this paper, we prove the existence of nontrivial solutions and ground state solutions for the following planar Schrödinger–Poisson system with zero mass − Δ u + ϕ u = ( I α ∗ F ( u ) ) f ( u ) , x ∈ R 2 , Δ ϕ = u 2 , x ∈ R 2 , where α ∈ ( 0 , 2 ), I α : R 2 → R is the Riesz potential, f ∈ C ( R , R ) is of subcritical exponential growth in the sense of Trudinger–Moser. In particular, some new ideas and analytic technique are used to overcome the double difficulties caused by the zero mass case and logarithmic convolution potential.

Wave run-up on surface-piercing columns is an important phenomenon in offshore engineering. Previous studies have mainly focused on a single column and circular column arrays. This study is concerned with the wave run-up ratio and the wave force on a fixed array of four rounded square columns. A series of regular wave tests were conducted, and the effects of wave periods and steepness were investigated. The nonlinearity of the wave run-up under incident waves with a small period is more sensitive to wave steepness. Utilizing empirical mode decomposition (EMD) and fast Fourier transform (FFT) methods, the measured signals were separated into three components representing characteristics of the incident wave component (IMF1), near-field interference (IMF2), and far-field low frequency reflected wave (IMF3), respectively. The proposed methods are helpful for studying the mechanism of near-field interference, and the experimental data are essential benchmarks for validating further numerical simulations of wave run-ups on rounded square columns.

Investigated in the present paper is a fifth-order nonlinear evolution (FONLE) equation, known as a nonlinear water wave (NLWW) equation, with applications in the applied sciences. More precisely, a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain. The Kudryashov methods (KMs) are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W -shaped and other solitons. In the end, the effect of changing the coefficients of nonlinear terms on the dynamical features of W -shaped and other solitons is investigated in detail for diverse groups of the involved parameters.

This article presents a circuit model that is able to capture the full nonlinear behavior of an asymmetric electrostatic transducer whose dynamics are governed by a single degree of freedom. Effects such as stress-stiffening and pull-in are accounted for. The simulation of a displacement-dependent capacitor and a nonlinear spring is accomplished with arbitrary behavioral sources, which are a standard component of circuit simulators. As an application example, the parameters of the model were fitted to emulate the behavior of an electrostatic MEMS loudspeaker whose finite-element (FEM) simulations and acoustic characterisation where already reported in the literature. The obtained waveforms show good agreement with the amplitude and distortion that was reported both in the transient FEM simulations and in the experimental measurements. This model is also used to predict the performance of this device as a microphone, coupling it to a two-stage charge amplifier. Additional complex behaviors can be introduced to this network model if it is required.

A novel approximate analytical solution to the linear damped Kawahara equation using a suitable hypothesis is reported for the first time. Based on the exact solutions (such as solitary waves, cnoidal waves, etc.) of the undamped Kawahara equation, the dissipative nonlinear structures like dissipative solitons and cnoidal waves are investigated. The obtained solution is considered a general solution, i.e., it can be applied for studying the properties of all dissipative traveling waves described by the linear damped Kawahara equation. Our technique is not limited to solve the linear damped Kawahara equation only, but it can be used for solving a large number of non-integrable evolution equations related to the realistic natural phenomena. Moreover, the maximum global residual error in the whole space-time domain is estimated for checking the accuracy of the obtained solutions. The obtained solutions can help many researchers in explaining the ambiguities about the mechanisms of propagation of nonlinear waves in complex systems such as seas, oceans, plasma physics, and much more.

Expansion of power grids has resulted in the construction of multiple transmission lines within constrained spaces inevitably making them nonuniform in nature. Existing transmission line models available in electromagnetic transient (EMT) simulators are based on classical multiconductor transmission line (MTL) theory with the assumption that the transmission lines are infinitely long and have uniform cross-sectional dimensions. This paper develops a time-domain model, namely dispersive scattered field transmission line (DSFTL) model, for multiconductor dispersive nonuniform overhead transmission lines above lossy, frequency-dependent ground. The proposed model which consists of closed-form equations in the time-domain has been implemented using a modified finite-difference time-domain (MFDTD) algorithm and integrated into an EMT simulator (PSCAD/EMTDC). Results have been compared with and verified by those obtained using a full-wave approach and measured data available in the literature. Simulations of nonuniform structures that include nonlinear components (such as breakers) have also been carried out under fault conditions.

Three-phase four-leg four-wire (3P4L4W) three- level (3L) inverters have the ability to supply both balanced and unbalanced loads. This letter establishes common-mode (CM) and differential-mode (DM) circuit models for the 3P4L4W 3L inverter. The 3L phase-leg CM voltage is determined by the voltage balancing control (VBC) for the split dc-bus voltages, that the DM load voltages are subject to the DM voltage control for the 3L phase-leg, and that the CM load-voltage is subject to the control for the fourth phase-leg. On this basis, a decoupled modulation is proposed where the 3L phase-legs are modulated to attain VBC and closed-loop DM load-voltage control, whereas the fourth phase-leg is independently modulated to realize the closed-loop CM load-voltage control. The proposed work has been experimentally verified, showing that the 3P4L4W 3L inverter with this decoupled modulation scheme can provide well-balanced ac load voltages and low total harmonic distortion (THD) for any type of ac loads: balanced, unbalanced, linear, and nonlinear.

The (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis is described by the space-time fractional Calogero-Degasperis (CD) and fractional potential Kadomstev-Petviashvili (PKP) equation. It can be modeled according to the Hamiltonian structure, the lax pair with the non-isospectral problem, and the pain level property. The proposed equations are widely used in beachfront ocean and coastal engineering to describe the propagation of shallow-water waves, demonstrate the propagation of waves in dissipative and nonlinear media, and reveal the propagation of waves in dissipative and nonlinear media. In this paper, we have established further exact solutions to the nonlinear fractional partial differential equation (NLFPDEs), namely the space-time fractional CD and fractional PKP equations using the modified Rieman-Liouville fractional derivative of Jumarie through the two variable ( G ′ / G , 1 / G )-expansion method. As far as trigonometric, hyperbolic, and rational function solutions containing parameters are concerned, solutions are acquired when unique characteristics are assigned to the parameters. Subsequently, the solitary wave solutions are generated from the solutions of the traveling wave. It is important to observe that this method is a realistic, convenient, well-organized, and ground-breaking strategy for solving various types of NLFPDEs.

This work investigates three nonlinear equations that describe waves on the oceans which are the Kadomtsev Petviashvili-modified equal width (KP-MEW) equation, the coupled Drinfel’d-Sokolov-Wilson (DSW) equation, and the Benjamin-Ono (BO) equation using the modified ( G ′ G 2 ) -expansion approach. The solutions of proposed equations by modified ( G ′ G 2 ) -expansion approach can be trigonometric, hyperbolic, or rational solutions. As a result, some new exact solutions are obtained and plotted.

This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burgers–Hilbert equation derived by Biello and Hunter (2010) using formal asymptotic expansions. The proof uses a modified energy method to show that the contour dynamics equations for vorticity fronts in the Euler equations and the Burgers–Hilbert equation are both approximated by the same cubically nonlinear asymptotic equation. The contour dynamics equations for Euler vorticity fronts are also derived.

A sliding mode control (SMC) strategy is proposed in this paper for a class of perturbed nonlinear systems with unmeasurable states and state constraints to deal with the state tracking problems. First of all, a partial states observer is designed for solving the problems due to unmeasurable states. The estimation errors will approach zero in a finite time. Secondly, based on a designed barrier Lyapunov function, one designs the sliding surface function and an adaptive sliding mode tracking controller to ensure that the states have the ability to track the desired signals. Moreover, the tracking error is capable of converging to zero in a finite time without violating the given state's constraints. Perturbation estimator and adaptive mechanisms are also utilized so that there is no need to know the upper bounds of perturbations and perturbation estimation errors. Finally, a numerical example is provided to demonstrate the feasibility of the proposed control strategy.

The large-amplitude free vibrations of an inextensible tapered beam with inertia and static nonlinearities were investigated using the continuous piecewise linearization method (CPLM). The CPLM solution was found to be in excellent agreement with exact numerical solutions and more accurate than other published approximate solutions. The study focuses on the large-amplitude vibrations where the nonlinear effects are strong and the response is characterized by anharmonicity. The present investigation showed that the CPLM solution predicted the anharmonic response due to strong nonlinearity whereas the other published solutions showed large errors. The effects of inertia and static nonlinearities were investigated and it was observed that an increase in the static nonlinear stiffness increases the vibration frequency whereas an increase in inertia nonlinearity reduces vibration frequency. Also, the combined effect of the inertia and static nonlinearities on the large-amplitude vibration response was investigated. It was observed that an increase in the ratio of the static to inertia nonlinearity increases the vibration frequency and vice versa.

This paper presents the effects of encoder errors caused by the mechanical torsional vibrations on the characteristics of the thrust force for the permanent magnet linear motor (PMLM) motion system. Firstly, the effects of the mechanical vibrations on the encoder errors are analyzed. Then the three-phase current is calculated considering the nonlinearity of the drive circuit. Based on the Maxwell's equations and Schwarz-Christoffel(SC) method, the analytical model of the magnetic field in air-gap is established taking into account the slot effect. Finally, the thrust force considering the encoder errors is analytically presented using the electromagnetic energy method, and the experimental verification is carried out. The results show that the mechanical torsional vibrations will produce different kinds of encoder errors for the optical linear encoder. These encoder errors will be coupled with the harmonics in the magnetic field. Consequently, lots of new thrust harmonics appear, affecting the characteristics of the thrust force and the performance of the PMLM motion system.

The (3+1)-dimensional Kadomtsev-Petviashvili and the modified KdV-Zakharov-Kuznetsov equations have a significant impact in modern science for their widespread applications in the theory of long-wave propagation, dynamics of shallow water wave, plasma fluid model, chemical kinematics, chemical engineering, geochemistry, and many other topics. In this article, we have assessed the effects of wave speed and physical parameters on the wave contours and confirmed that waveform changes with the variety of the free factors in it. As a result, wave solutions are extensively analyzed by using the balancing condition on the linear and nonlinear terms of the highest order and extracted different standard wave configurations, containing kink, breather soliton, bell-shaped soliton, and periodic waves. To extract the soliton solutions of the high-dimensional nonlinear evolution equations, a recently developed approach of the sine-Gordon expansion method is used to derive the wave solutions directly. The sine-Gordon expansion approach is a potent and strategic mathematical tool for instituting ample of new traveling wave solutions of nonlinear equations. This study established the efficiency of the described method in solving evolution equations which are nonlinear and with higher dimension (HNEEs). Closed-form solutions are carefully illustrated and discussed through diagrams.

An extended FitzHugh–Nagumo model is developed to model the synaptic coupling of neurons and the associated dynamics. The neurons are coupled via chemical synapses, which can excite or inhibit the postsynaptic neuron. The neurotransmitter-receptor dynamics is governed with a gating dynamic, which allows for the distinction between fast and slow synapses. Detailed nonlinear dynamics analysis are performed for simple neural motifs of a self-synapsed neuron and two synaptically coupled neurons for the instabilities that lead to neural oscillations, and the associated phase diagrams are obtained. Interesting dynamics such as synchronization of fast and slow firing neurons, frequency enhancement, quiescent neurons coupled to oscillators, chaotic spiking, and periodic bursting are found.

Based on three-wave method, abundant nonautonomous solutions with different wave structures of a 3D variable-coefficient generalized shallow water wave equation are presented. In this situation the basic configurations (characteristic, amplitude, and speed) of the nonautonomous waves mutate with time due to the effect of nonlinearity and dispersion. Discussions indicate the interaction between lump wave and a pair of resonance stripe solitons solutions, the interaction between lump wave and periodic wave solutions, and the breather-type periodic soliton solutions. The dynamic properties of the obtained solutions are demonstrated and analyzed graphically for different choices of the arbitrary functions in these solutions.

This work aims to present nonlinear models that arise in ocean engineering. There are many models of ocean waves that are present in nature. In shallow water, the linearization of the equations requires critical conditions on wave capacity than it make in deep water, and the strong nonlinear belongings are spotted. We use Lie symmetry analysis to obtain different types of soliton solutions like one, two, and three-soliton solutions in a (2+1) dimensional variable-coefficient Bogoyavlensky Konopelchenko (VCBK) equation that describes the interaction of a Riemann wave reproducing along the y-axis and a long wave reproducing along the x-axis in engineering and science. We use the Lie symmetry analysis then the integrating factor method to obtain new solutions of the VCBK equation. To demonstrate the physical meaning of the solutions obtained by the presented techniques, the graphical performance has been demonstrated with some values. The presented equation has fewer dimensions and is reduced to ordinary differential equations using the Lie symmetry technique.

This paper investigates the air-gap field distribution of the permanent-magnet vernier machine (PMVM) using nonlinear exact conformal model (NECM) to account for slotting effect, flux modulation effect and iron nonlinearity. The exact conformal model based on the region of one-slot and one-flux-modulation-pole (OSECM) are introduced to show the effectiveness of linear analytical model for PMVM. It can keep high calculation accuracy and significantly reduce the computational burden. Then, the NECM is developed from OSECM by introducing the equivalent saturation current into the air region and coil region. The lumped parameter magnetic circuit model (LPMCM) model is used to obtain the magnetic potential of iron region and therefore calculate the equivalent saturation current. The NECM which combines LPMCM and OSECM can essentially improve the accuracy of linear analytical model. The harmonic analysis of air-gap field is performed to theoretically explain the component of electromagnetic torque. Both finite element model (FEM) simulation and test results are presented to validate the NECM.

Convection differential equations that include momentum, energy and mass balance equations are used for the simulations of boundary layer (BL) flows. In convection analysis, it is in execution to dimensionless the BL system through similarity variable. However, a wide range of convection differential equations cannot be non-dimensionalized using similarity variable therefore the intent of this manuscript is to develop non-similar model for the forced convective magnetic flow of a viscous fluid above an exponentially expanding surface saturated by nano-fluid. The non-similarity is due to the exponential stretching of the surface and viscous dissipation. Influences of chemical reaction and heat generation are also incorporated. The non-similarity transformation is applied to the nonlinear partial differential system (PDE’s) to transform them into dimensionless PDE’s. Non-similar system is analytically approximated by adapting local non-similarity (LNS) and then it is numerically simulated by finite difference based bvp4c algorithm to explore the influences of significant numbers named as Prandlt number, chemical reaction, magnetic field, Brownian motion, heat generation, Eckert number, thermophoresis on concentration, velocity and temperature distribution. Auxiliary consequences presume that the heat penetration in fluid rises with enhancements in Brownian motion and Prandtl number, while it can be perceived here that for positive estimations of heat generation causes the thicker temperature field. Increasing non-similarity variable and magnetic number become reason for the reduction of temperature profile and chemical reaction is reason of reduced concentration profile.

Vibrational control seeks to stabilize an unstable system by judiciously injecting a state-free high-frequency dither. This paper presents some robustness properties of vibrational control with respect to additive disturbances in a nonlinear system. We assume that, without disturbances, the appropriately averaged system is regionally asymptotically stable. Using perturbation techniques, our first result shows that the stabilization realised through vibrational control is robust with respect to additive disturbances of sufficiently small amplitude. Indeed, the perturbed system of vibrational control has a robustness feature similar to input-to-state stability in a local region. In the case of periodic disturbances, our second result indicates that vibrational control naturally dampens disturbances of sufficiently high frequency, which allows for relatively high amplitude disturbances. A tight bound for the effect of such periodic disturbances on the ultimate deviation of states from the desired equilibrium is presented. Simulation results from a planar manipulator support the theoretic analysis.

The crystal structure of a solid largely dictates its electronic, optical and mechanical properties. Indeed, much of the exploration of quantum materials in recent years including the discovery of new phases and phenomena in correlated, topological and two-dimensional materials—has been based on the ability to rationally control crystal structures through materials synthesis, strain engineering or heterostructuring of van der Waals bonded materials. These static approaches, while enormously powerful, are limited by thermodynamic and elastic constraints. An emerging avenue of study has focused on extending such structural control to the dynamical regime by using resonant laser pulses to drive vibrational modes in a crystal. This paradigm of ‘nonlinear phononics’ provides a basis for rationally designing the structure and symmetry of crystals with light, allowing for the manipulation of functional properties at high speed and, in many instances, beyond what may be possible in equilibrium. Here we provide an overview of the developments in this field, discussing the theory, applications and future prospects of optical crystal structure engineering. The interaction between light and the crystal lattice of a quantum material can modify its properties. Utilizing nonlinear interactions allows this to be done in a controlled way to design specific non-equilibrium functionalities.

Static black hole with the Power Maxwell invariant (PMI), Born–Infeld (BI), logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional spacetime with cosmological constant was studied. It was shown that the LN and EN fields represent the Born–Infeld type of nonlinear electrodynamics. It the framework of General Relativity the exact solutions of the field equations were obtained, corresponding thermodynamic functions were calculated and the [Formula: see text] criticality of the black holes in the extended phase-space thermodynamics was investigated.

We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The model supports a steady parallel shear flow as a response to the wind stress. As the maximal velocity of the shear flow (equivalently the maximal amplitude of the wind forcing) exceeds a critical threshold, the zonal jet destabilizes due to baroclinic instability and we numerically demonstrate that a first transition occurs. We obtain reduced equations of the system using the formalism of dynamic transition theory and establish two scenarios which completely describe this first transition. The generic scenario is that two modes become critical and a Hopf bifurcation occurs as a result. Under an appropriate set of parameters describing midlatitude oceanic flows, we show that this first transition is continuous: a supercritical Hopf bifurcation occurs and a stable time periodic solution bifurcates. We also investigate the case of double Hopf bifurcations which occur when four modes of the linear stability problem simultaneously destabilize the zonal jet. In this case we prove that, in the relevant parameter regime, the flow exhibits a continuous transition accompanied by a bifurcated attractor homeomorphic to $S^3$. The topological structure of this attractor is analyzed in detail and is shown to depend on the system parameters. In particular, this attractor contains (stable or unstable) time-periodic solutions and a quasi-periodic solution., Comment: 20 pages, 12 figures, 2 tables

In this work, the improved modified extended tanh scheme is implemented to extract exact travelling wave solutions for perturbed nonlinear Schrodinger’s equation with Kudryashov’s law of refractive index and dual form of generalized nonlocal nonlinearity. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic wave solutions, periodic wave solutions, Jacobi elliptic functions, plane wave and hyperbolic wave solutions. Moreover, 3D and contour plots of some solutions are illustrated to show the physical nature of obtained solutions.

Introduction The Gross-Pitaevskii equation is a class of the nonlinear Schrodinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in the intersection field of Bose-Einstein condensate with some other fields. It is an important subject to investigate their exact solutions. Objectives We give multi-soliton of a two-dimensional Gross-Pitaevskii system which contains the time-varying trapping potential with a few interactions of multi-soliton. Through analytical and graphical analysis, we obtain one-, two- and three-soliton which are affected by the strength of atomic interaction. The asymptotic expression of two-soliton embodies the properties of solitons. We can give some interactions of solitons of different structures including parabolic soliton, line-soliton and dromion-like structure. Methods By constructing an appropriate Hirota bilinear form, the multi-soliton solution of the system is obtained. The soliton elastic interaction is analyzed via asymptotic analysis. Results The results in this paper theoretically provide the analytical bright soliton solution in the two-dimensional Bose-Einstein condensation model and their interesting interaction. To our best knowledge, the discussion and results in this work are new and important in different fields. The results enrich the existing nonlinear phenomena of the Gross-Pitaevskii model in Bose-Einstein condensation, and prove that the Hirota bilinear method and asymptotic analysis method are powerful and effective techniques in physical sciences and engineering for analyzing nonlinear mathematical-physical equations and their solutions. These provide a valuable basis and reference for the controllability of bright soliton phenomenon in experiments for high-dimensional Bose-Einstein condensation.

A novel method for close-proximity formation flying under differential atmospheric drag using Coulomb forces is investigated for applications in Earth sensing, space-situational awareness (SSA), and aeronomy. Objects in LEO are supersonic with respect to the ambient environment, creating a thinned out wake region behind the craft as it travels through the ionosphere. Objects within this wake experience little drag acceleration and are able to attain voltages much greater than in the ambient ionospheric plasma, creating implications for the design and control of close-proximity leader–follower spacecraft pairs. The proposed system consists of a leader craft with a set of affixed, conducting spheres and a charged follower craft located in the wake of the leader. The differential drag acceleration between the leader and follower craft is countered by a controlled Coulomb repulsion to maintain precise separation. The charged structure on the rear of the leader craft is designed such that the charged follower craft sits in an electrostatic potential well which opposes off-axis perturbations. A conceptual method for controlling such a pair without the use of propellant using a set of charged spheres is investigated, with nonlinear models of the system’s relative motion derived and discussed. Linearized models are used to demonstrate the local controllability of the system to demonstrate the proposed system’s merit. This linear analysis is used to derive conditions on controllability and control performance under different charge geometries and environmental assumptions.

Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period, and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method, and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.