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The primary objective of this study aims to carry out a more thorough investigation into a fractional nonlinear double dispersive equation that is used to represent wave propagation in an elastic, inhomogeneous Murnaghan's rod. By Murnaghan's rod, we mean the materials, which include the constitutive constant, Poisson ratio, and Lame'́s coefficient, are considered to be compressible in nature forming up the elastic rod. To solve the fractional version of Murnaghan's rod problem, we employed β -fractional and M -Truncated fractional derivative. Regarding the extraction of polynomial and rational function solutions of the Murnaghan's rod problem, which degenerate into several wave solutions including solitary, soliton (dromions), as well as periodic wave solutions. We employ the well-known unified and new auxiliary equation methods of nonlinear sciences. A finite series of certain functions satisfying an ordinary differential equation of first order, second degree is used to represent the projected solution. Based on the given approach, numerous types of solutions for exponential, hyperbolic, and trigonometric functions are generated. In this research study, the behavior of a dynamical planer system has been examined by giving various values to parameters and by depicting every possible situation as a phase portrait. The sensitivity analysis, where the soliton wave velocity and wave number parameters influence the water wave singularity, is demonstrated using the wave profiles of the constructed dynamical structural system. With the use of graphs, we have simulated the solitons to determine their kinds. All of solutions found in this manuscript is been confirmed through back substituting them into the original model using computational software. • An investigation to the wave propagation in an elastic, inhomogeneous Murnaghan's rod is considered. • The solutions under Beta and M-Truncated fractional derivatives for this model were found by two different analytical techniques. • The behavior of the dynamical planer system has been examined by depicting every possible situation as a phase portrait. • The sensitivity analysis is demonstrated using the wave profiles of the constructed dynamical structural system. [ABSTRACT FROM AUTHOR]

• New solitons solutions for two different nonlinear models were constructed. • The solutions of these models were found using the rational (G'/G,1/G)-expansion technique. • The Physical meaning for the obtained solutions is graphically investigated. In the electrical transmission lines, the processing of cable signals distribution, computer networks, high-speed computer databases and discrete networks can be investigated by the modified Zakharov-Kuznetsov (mZK) equation as a data link propagation control model in the study of nonlinear Schrödinger type equations as well as in the analysis of the generalized stationary Gardner equation. The proposed Gerdjikov–Ivanov model can be used in the field of nonlinear optics, weakly nonlinear dispersion water waves, quantum field theory etc. In this work, we developed complete traveling wave solutions with specific t-type, kink type, bell-type, singular solutions, and periodic singular solutions to the proposed mZK equation and the Gerdjikov-Ivanov equation with the aid of the double G ′ / G , 1 / G - expansion method. These settled solutions are very reliable, durable, and authentic which can measure the fluid velocity and fluid density in the electrically conductive fluid and be able to analysis of the flow of current and voltage of long-distance electrical transmission lines too. These traveling wave solutions are available in a closed format and make them easy to use. The proposed method is consistent with the abstraction of traveling wave solutions. [ABSTRACT FROM AUTHOR]

• New solitons solutions for the NLS and MTs models were constructed. • The performance is discussed through the generalized Kudryashov method. • The Physical meaning for some of the obtained solutions are graphically investigated. The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is used in this article to extract stable, generic, and wide-ranging soliton solutions, comprising hyperbolic, exponential, trigonometric, and some other functions, and retrieve diverse known soliton structures by balancing the effects of nonlinearity and dispersion. It is established by analysis and graphs that changing the included parameters changes the waveform behavior, which is largely controlled by nonlinearity and dispersion effects. The impact of the other parameters on the wave profile, such as wave speed, wavenumber, etc., has also been covered. The results obtained demonstrate the reliability, efficiency, and capability of the implemented technique to determine wide-spectral stable soliton solutions to nonlinear evolution equations emerging in various branches of scientific, technological, and engineering domains. [ABSTRACT FROM AUTHOR]

This paper employs the Lie symmetry analysis to investigate novel closed-form solutions to a (2+1)-dimensional Bogoyavlenskii's breaking soliton equation. This Lie symmetry technique, used in combination with Maple's symbolic computation system, demonstrates that the Lie infinitesimals are dependent on five arbitrary parameters and two independent arbitrary functions f 1 (t) and f 2 (t). The invariance criteria of Lie group analysis are used to construct all infinitesimal vectors, commutative relations of their examined vectors, a one-dimensional optimal system and then several symmetry reductions. Subsequently, Bogoyavlenskii's breaking soliton (BBS) equation is reduced into several nonlinear ODEs by employing desirable Lie symmetry reductions through optimal system. Explicit exact solutions in terms of arbitrary independent functions and other constants are obtained as a result of solving the nonlinear ODEs. These established results are entirely new and dissimilar from the previous findings in the literature. The physical behaviors of the gained solutions illustrate the dynamical wave structures of multiple solitons, curved-shaped wave–wave interaction profiles, oscillating periodic solitary waves, doubly-solitons, kink-type waves, W-shaped solitons, and novel solitary waves solutions through 3D plots by selecting the suitable values for arbitrary functional parameters and free parameters based on numerical simulation. Eventually, the derived results verify the efficiency, trustworthiness, and credibility of the considered method. • The Lie symmetry approach is used to investigate a (2+1)-dimensional Bogoyavlenskii's breaking soliton equation. • At the outset, we derived Lie infinitesimal generators, commutator, and adjoint tables for the BBS equation. • Some exact closed-form solutions are obtained using the Lie symmetry technique. • 3D graphics are used to demonstrate the various evolutionary dynamics of some invariant solutions. • In the field of innovative research and improvement, such investigations are strongly encouraged. [ABSTRACT FROM AUTHOR]

• The Konopelchenko-Dubrovsky and the Landau-Ginzburg-Higgs equation studied using the generalized Kudryashov technique. • The obtained solutions are analyzed graphically. • Concluded that the generalized Kudryashov technique is effective for solving nonlinear evolution equations. The (2 + 1)-dimensional Konopelchenko-Dubrovsky (KD) equation and the Landau-Ginzburg-Higgs (LGH) equation describe the nonlinear waves with weak scattering and long-range interactions between the tropical, mid-latitude troposphere, the interaction of equatorial and mid-latitude Rossby waves etc. This article studies the KD and LGH models stated earlier using the generalized Kudryashov technique. We obtained a variety of analytical solutions including unknown parameters. The figures of some of the obtained solutions are sketched with certain parameters. The derived results demonstrate the efficiency and reliability of the generalized Kudryashov technique for establishing systematic solutions to nonlinear evolution equations (NLEEs). [ABSTRACT FROM AUTHOR]

In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painlevé analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE by employing the Lie symmetry analysis. We formally derive bright, dark and singular soliton solutions of the model. Moreover, we investigate the stability of the corresponding dynamical system via using phase plane theory. Graphical representation of the obtained solitons and phase portrait are illustrated by using Maple software. • The Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect is investigated. • The Painlevé and Lie symmetry analysis are applied to that equation. • The stability of the corresponding dynamical system is discussed via phase plane theory. • A graphical representation of the obtained soliton solutions is presented. [ABSTRACT FROM AUTHOR]

• Stable solitary solutions have been developed for NLEEs related to optics and superconductivity. • The effects of linearity and nonlinearity on the dynamics of wave profiles have been interpreted. • Standard wave profiles including kink, bell-shape soliton, and periodic solitons have been found. • The 3D and contour plots are depicted to illustrate profile of the phenomena. In the field of quantum mechanics and fluid physics, especially in the study of nonlinear geometric optics and superconductivity, the Landau-Ginzburg-Higgs (LGH) and the (2 + 1)-dimensional Novikov-Veselov (NV) equations are two significant models. In this article, we have affirmed that wave profile changes with the change of the free parameters associated with them and are mainly dominated by linear effects. The effects of nonlinearity and wave speed on the wave contours have also been analyzed. On account of this, wave solutions are computed concerning rational, hyperbolic, and trigonometric structures balancing the exponents of linear and nonlinear terms of the highest order, from which scores of typical wave profiles including kink, bell-shape soliton, lump, and periodic waves have been extracted. The wave solutions are designated through extending the typical concept of the sine-Gordon expansion (SGE) method from the lower dimensional to the higher dimensional nonlinear evolution equations. This study establishes the capability of the stated method in solving both lower and higher dimensional nonlinear evolution equations. The solutions are analyzed by sketching figures for different values of related variables, and it is observed that the attributes of these solutions are pivotal in the selection of parameters. [ABSTRACT FROM AUTHOR]

In this article, the closed form general and standard solutions accessible in the literature of nonlinear evolution equation (NLEE), namely, the Fokas-Lenells (FL) equation is established by using the generalized Kudryashov approach. The implemented method extracts lots of new and compatible wave solutions involving unknown parameters and expressed in terms of exponential, trigonometric and hyperbolic functions. We explain the physical meaning of geometrical structures for some derived solutions by assigning definite values of the unspecified parameters. As an aftermath, diverse wave shapes including kink wave shape, flat kink wave shape, bell shape, anti-bell shape, singular bell shape along with bright, dark, singular solitary wave envelopes are properly developed. These nonlinear wave envelopes are frequently applicable in optical fibers. It has been established that the assigned techniques are general, efficient and straightforward and also it can be exerted to accomplish closed form solutions of diverse NLEEs originated in mathematical physics and engineering fields. [ABSTRACT FROM AUTHOR]