Rouge wave solutions of a nonlinear pseudo-parabolic physical model through the advance exponential expansion method

In this work, we decide the proliferation of nonlinear voyaging wave answers for the dominant nonlinear pseudo-parabolic physical model through the (1+1)-dimensional Oskolkov equation. With the assistance of the advance -expansion strategy compilation of disguise adaptation an innovative version of interacting analytical solutions regarding, hyperbolic and trigonometric function with some refreshing parameters. We analyze the behavior of these solutions of Oskolkov equations for the specific values of the reared parameters such as rouge wave, multi solution, breather wave bell and kink shape etc. The dynamics nonlinear wave solution is examined and demonstrated in 3-D and 2-D plots with specific values of the perplexing parameters are plotted. The advance -expansion method solid treatment for looking through fundamental nonlinear waves that advance assortment of dynamic models emerges in engineering fields.

Characteristics of the lump, lumpoff and rouge wave solutions in a (3+1)-dimensional generalized potential Yu–Toda–Sasa–Fukuyama equation

In this work, we consider a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized nonlinear evolution equation, which can be reduced to the potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. We establish the more general lump solutions of the equation and discover its propagation path. It is interesting that we study the case where the lump wave is cut by one stripe wave. In this case, we obtain the lumpoff solution. Furthermore, the special rogue wave is generated by the collision of the lump wave and a couple of stripe soliton waves. The time and position it generates can be determined by tracking the propagation path of the lump wave. Finally, some graphical analysis of the solutions are presented to better understand the dynamic behavior of these waves.

Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

In this paper, we first present a complex multirational exp-function ansatz for constructing explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of nonlinear partial differential equations (PDEs) with complex coefficients. To illustrate the effectiveness of the complex multirational exp-function ansatz, we then consider a generalized nonlinear Schrödinger (gNLS) equation with distributed coefficients. As a result, some explicit rational exp-function solutions are obtained, including solitary wave solutions, N-wave solutions, and rouge wave solutions. Finally, we simulate some spatial structures and dynamical evolutions of the modules of the obtained solutions for more insights into these complex rational waves. It is shown that the complex multirational exp-function ansatz can be used for explicit solitary wave solutions, N-wave solutions, and rouge wave solutions of some other nonlinear PDEs with complex coefficients.

Stability analysis, soliton waves, rogue waves and interaction phenomena for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation is discussed, which can be used to describe certain characteristics of soliton in a nonlinear media with weak dispersion. By using the virtue of Bell polynomial, we construct the exact bilinear formalism and soliton wave of the equation, respectively. We also analyze its stability analysis. Moreover, based on the resulting bilinear formalism, we obtain its rouge wave solutions with a direct method. Finally, we also discuss the interaction phenomena between solitary wave solutions and rogue wave solutions. It is hoped that our results can be used to enrich the dynamics of the (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear wave fields.

Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

With the aid of symbolic computation, we derive new types of variable separation solutions for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation based on an improved mapping approach. Rich coherent structures like the soliton-type, rouge wave-type, and cross-like fractal type structures are presented, and moreover, the fusion interactions of localized structures are graphically investigated. Some of these solutions exhibit a rich dynamic, with a wide variety of qualitative behavior and structures that are exponentially localized.

Multidromion Soliton and Rouge Wave for the (2 + 1)-Dimensional Broer-Kaup System with Variable Coefficients

Broad new families of rational form variable separation solutions with two arbitrary lower-dimensional functions of the (2 + 1)-dimensional Broer-Kaup system with variable coefficients are derived by means of an improved mapping approach and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as rouge wave, multidromion soliton, and soliton vanish phenomenon are revealed by selecting appropriate functions of the general variable separation solution.