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Some bright wave solutions of the coupled derivative nonlinear Schrödinger(CDNLS) equations are derived with Riemann–Hilbert(RH) method. We observe some novel non-autonomous bright soliton structures by choosing the different nonlinear perturbation function g (t). It is shown that there are some possibilities to manipulate the interactions of non-autonomous wave solution through choosing nonlinear and gain/loss functions. Some dynamic behaviors of interactions between two bright solitons have been asymptotically analyzed, the two parabolic-type bright solitons propagate with the opposite directions after the interaction. And some interactions of the linear-, parabolic- and periodic-type bright two-solitons are elastic. A general approach is presented to manipulate soliton waves, which has the potential application for the optical self-routing, non-Kerr media and Bose–Einstein condensates(BEC). [ABSTRACT FROM AUTHOR]

Abstract A generalized nonlocal nonlinear Gross–Pitaevskii(GP) equation is presented, which can be reduced to the nonlocal GP equation with self-induced PT -symmetric potential. We derive some novel non-autonomous soliton solutions of nonlocal GP equation via inverse scattering and similarity transformations. These obtained solutions have singularities and are not the standard soliton solutions, here they can be called soliton-like(SL) solutions. Then we consider some controllable behaviors of these non-autonomous wave solutions. The obtained results are different from the solutions of the local nonlinear GP equation. Some propagation phenomena are produced through manipulating non-autonomous SL waves, which can present the potential applications to the soliton wave phenomena in nonlocal wave models. [ABSTRACT FROM AUTHOR]

Abstract We consider the Gross–Pitaevskii(GP) equation with the combination of periodic and harmonic external potentials. In particular, the method of inverse scattering transformation is applied to the GP equation with external potentials. Furthermore, some exact soliton solutions are obtained for the GP equation by using inverse scattering transformation, in which some physically relevant bright solutions are described. The stabilities of the obtained matter-wave solutions are addressed numerically such that some stable solutions are found, and some solitons can be stable in a wide region. These results may raise the possibility of relative experiments and potential applications. [ABSTRACT FROM AUTHOR]

We present the generalized Gross–Pitaevskii (GP( p , q )) equation with two kinds of specific space–time modulated potentials, including the generalized Rosen–Morse potential, the combination of harmonic and Gaussian (harmonic–Gaussian) potential. Some analytical bright soliton solutions are derived from the generalized GP( p , q ) equation via the complex similarity transformation and the generalized stationary nonlinear Schrödinger (NLS) equation. The soliton solutions can be reduced to Jacobi elliptic and spikon-like solutions by choosing the different parameters, and describe some physically relevant phenomenons. Furthermore, some stabilities of the obtained matter-wave solutions are addressed numerically. We find that some solutions are stable and can be observed over a broad range of parameters through analyzing the effect of the phase noise on these solutions. The obtained results may give a certain theoretical guiding significance of relative experiments in Bose–Einstein condensates. [ABSTRACT FROM AUTHOR]

Abstract: A kind of nonlinear integrable couplings of C-KdV soliton hierarchy is constructed, then we present the infinitely many conservation laws for the nonlinear integrable couplings of the C-KdV soliton hierarchy. [Copyright &y& Elsevier]

Abstract: In this paper, we construct explicit rogue wave solutions and dark-bright solutions for the inhomogeneous coupled nonlinear Schrödinger equation with variable coefficients by means of similarity transformations. Some explicit solutions to the coupled nonlinear Schrödinger equation with potentials and nonlinearities depending on both time and spatial coordinates are considered. We present the general approach and use it to calculate rogue wave solutions and dark-bright solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics. [Copyright &y& Elsevier]

Abstract: In this paper, the rational solutions with arbitrary constants of a Hirota equation are presented employing the Darboux transformations. Then, the similarity transformation allows us to relate certain class of multi-rogue wave solutions of the higher-order nonlinear Schrödinger equation (NLSE) to the solutions of (1+1)-dimensional integrable Hirota equation. The multi-rogue wave solutions with arbitrary constants are considered. The obtained rogue wave solutions can be used to describe the possible formation mechanisms for optical and Bose–Einstein condensates. [Copyright &y& Elsevier]

Abstract: A three-dimensional Gross–Pitaevskii (3D-GP) equation with time variable coefficients is considered, and is transformed into a standard nonlinear Schrödinger (NLS) equation. We study exact solutions of the 3D-GP equation with (space, time)-modulated potential and nonlinearity. In particular, based on the similarity transformation, we report several families of exact solutions of the 3D-GP equation with different amplitude surfaces, in which some physically relevant solutions are described. These results may raise the possibility of relative experiments and potential applications. [Copyright &y& Elsevier]

Abstract: In this paper, we present an integrable coupling of lattice hierarchy and its continuous limits by using Lie algebra . By introducing a complex discrete spectral problem, the integrable coupling of Kac–Van Moerbeke lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable coupling of discrete soliton equation hierarchy, which has the integrable coupling system of MKdV hierarchy as a new kind of continuous limit. [Copyright &y& Elsevier]

Abstract: We present a new method to construct two (2+1)-dimensional lattice hierarchies. By considering a kind of spectral problems with two shift operators and , a new (2+1)-dimensional discrete soliton hierarchy and a new lattice hierarchy are constructed by using matrix spectral problem. [Copyright &y& Elsevier]

Abstract: A generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using differential forms and exterior derivatives of fractional orders. We construct the generalized fractional trace identity through the Riemann–Liouville fractional derivative. An example of the fractional KN soliton equation hierarchy and Hamiltonian structure is presented, which is a new integrable hierarchy and possesses Hamiltonian structure. [Copyright &y& Elsevier]

Abstract: Based on the Kupershmidt deformation, we propose the generalized Kupershmidt deformation (GKD) to construct new systems from integrable bi-Hamiltonian system. As applications, the generalized Kupershmidt deformation of the fifth-order coupled KdV equations hierarchy with self-consistent sources and its Lax representation are presented. [Copyright &y& Elsevier]

Abstract: We present a kind of integrable couplings of soliton equations hierarchy with self-consistent sources by using the loop algebra . As an application, a new integrable couplings of the generalized Wadati–Konono–Ichikawa (G-WKI) equations hierarchy with self-consistent sources is derived through the enlarged loop algebra . [Copyright &y& Elsevier]

Abstract: A noncommutative version of the TC soliton equation hierarchy is presented, which possesses the zero curvature representation. Then, we show that noncommutative (NC) TC equation can be derived from the noncommutative (anti-)self-dual Yang–Mills equation by reduction. Finally, an integrable coupling system of the NC TC equation hierarchy is constructed by using of the enlarged Lax pairs. [Copyright &y& Elsevier]

Abstract: In this paper we present a soliton hierarchy of vector KN (Kaup–Newell) equations by using an arbitrary order matrix spectral problem, along with its bi-Hamiltonian formulation. Then, adjoint symmetry constraints are presented for manipulating binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the vector KN equations. Finally, a class of integrable coupling systems of the vector KN soliton equations is obtained through enlarging the spectral problem. [Copyright &y& Elsevier]

Abstract: A kind of non-isospectral integrable couplings of discrete soliton equations hierarchy with self-consistent sources associated with [Y.F. Zhang, E.G. Fan, Characteristic Numbers of Matrix Lie Algebras, Commun. Theor. Phys (China) 49 (2008) 845] is presented. As an application example, the hierarchy of non-isospectral cubic Volterra lattice hierarchy with self-consistent sources is derived. Furthermore, we construct a non-isospectral integrable couplings of cubic Volterra lattice hierarchy with self-consistent sources by using the loop algebra . [Copyright &y& Elsevier]

Abstract: A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra . It follows that an isospectral problem is established. By use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component Yang hierarchy is given. Finally, the multi-component super-integrable coupling system of Yang hierarchy is presented by enlarging matrix spectral problem. [Copyright &y& Elsevier]

Abstract: A kind of the integrable couplings of soliton equations hierarchy with self-consistent sources associated with is presented. As an application example, we construct a new integrable couplings of the Dirac soliton hierarchy with self-consistent sources by using of loop algebra . [Copyright &y& Elsevier]

Abstract: A new subalgebra of loop algebra is first constructed. It follows that an isospectral problem is established. Using Tu-pattern gives rise to a new integrable hierarchy, which possesses bi-Hamiltonian structure. Furthermore, by making use of bi-symmetry constraints, the generalized Hamiltonian regular representations for the hierarchy are obtained. Finally, we obtain an expanding integrable system of this hierarchy by applying a scalar transformation between two isospectral problems and constructing a five-dimensional loop algebra . [Copyright &y& Elsevier]

Abstract: The generalized zero curvature equation is presented, which is an important tool to construct the (2+1)-dimensional integrable soliton equation hierarchy. A few of new (2+1)-dimensional integrable soliton equation hierarchies are obtained through the generalized zero curvature equation. [Copyright &y& Elsevier]

Abstract: In this paper, we first present a fractional Hamiltonian function. Then, based on the dissipative Hamiltonian realization, using the fractional Hamiltonian function method, as a static measurable feedback, a criterion for the fractional nonlinear differential algebraic systems (FNDAS) is proposed to stabilize the multi-machine power system. Finally, FNDAS in presence of disturbance, a fractional H ∞ control strategy is constructed. The proposed stabilization and robust controller can effectively take advantage of the structural characteristics of FNDAS and is simple in form. [Copyright &y& Elsevier]

Abstract: A scheme for deducing Hamiltonian structures of the integrable couplings for the multicomponent hierarchies of evolution equations is presented, which is devoting to obtaining the Hamiltonian structures of the integrable couplings of the multicomponent Dirac hierarchy. [Copyright &y& Elsevier]

Abstract: A fractional order soliton equation hierarchy is presented, which is a new Liouville integrable hierarchy and possesses bi-Hamiltonian structure. Finally, we obtain a integrable coupling system of this fractional order soliton equation hierarchy by applying a upper triangular matrix of Lie algebras. [Copyright &y& Elsevier]

Abstract: In this article by considering a multi-dimensional Lie algebra system, a new multi-function integrable equation hierarchy is presented with the help of MAPLE. Then the integrable coupling system of the new multi-function integrable equation hierarchy is obtained through enlarging matrix spectral problem. [Copyright &y& Elsevier]

Abstract: In this Letter by considering a -dimensional discrete non-isospectral linear problem, a new -dimensional integrable lattice hierarchy is constructed. It shows that generalization of the Blaszak–Marciniak lattice hierarchy can be obtained as a reduction. Then an extended algebraic system of X is presented, from which the integrable coupling system of the -dimensional discrete non-isospectral Blaszak–Marciniak lattice equations are obtained. [Copyright &y& Elsevier]

Abstract: The quadratic trace identity is presented, which is devoted to constructing the Hamiltonian structures of some multicomponent equation hierarchies. [Copyright &y& Elsevier]

Until now, the soliton solutions of nonlocal equations have also been put forward for the corresponding local equations. However, a natural motivation of our work is to find some soliton solutions to the mixed local–nonlocal equations that have not been reported for the associated nonlocal-type equations. A novel mixed local–nonlocal nonlinear Schrödinger (MLN-NLS) equation is presented, then we investigate the Hirota's bilinearization transformation and obtain the one- and two-soliton solutions of the MLN-NLS equation. Based on the obtained solutions, the propagation and interaction structures are shown, the broken and unbroken soliton solutions are derived with Hirota's transformation. We find that the MLN-NLS equation has some novel results, which is unlike the local or nonlocal cases. And these results seem to be the characteristic features of the mixed local–nonlocal nonlinear system in the present work. [ABSTRACT FROM AUTHOR]

The diffraction problem of a concentric truncated cylinder system with a porous ring plate fixed inside is studied in the framework of linear potential theory. The system consists of a porous exterior cylinder and an impermeable interior cylinder, which are connected by an impermeable top and bottom plate, and a porous ring plate arranged below the free surface. Darcy's law is applied to the porous boundaries under the assumption of fine pores. The velocity potential of the whole fluid domain is analytically derived by the method of variable separation and eigen-function expansion. The hydrodynamic loads of the system are obtained by integrating the pressure on the wet surface. The calculation results of the present paper are compared with the previous works with similar models to verify the correctness of the model. The effect of the dimensionless porous effect parameter of the ring plate and of the exterior cylinder, the draft–depth ratio of the ring plate, the draft–depth ratio of the system, the ratio of the interior and exterior radii are discussed. The results show that appropriate permeability and structural scale parameters can improve the hydrodynamic performance of the structure, which will provide directive guidance for engineering design. • The wave diffraction from a concentric truncated cylinder system was studied. • The theory and program were validated by similar models in previous works. • The effect of some parameters on the hydrodynamic performance was discussed. [ABSTRACT FROM AUTHOR]