Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation

Sixing Tao; Sixing Tao

doi:10.3934/math.2022864

AIMS Mathematics

2022, Volume 7, Issue 9: 15795-15811. doi: 10.3934/math.2022864

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Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation

Sixing Tao ^,

School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China

Received: 13 May 2022 Revised: 15 June 2022 Accepted: 18 June 2022 Published: 27 June 2022
MSC : 35A25, 35G50, 35Q35, 37K10

In this paper, a (3+1)-dimensional nonlinear evolution equation is considered. First, its bilinear formalism is derived by introducing dependent variable transformation. Then, its breather wave solutions are obtained by employing the extend homoclinic test method and related figures are presented to illustrate the dynamical features of these obtained solutions. Next, its resonant multi-soliton solutions are obtained by using the linear superposition principle. Meanwhile, 3D profiles and contour plots are presented to exhibit the process of wave motion. Finally, M-breather wave solutions such as one-breather, two-breather, three-breather and hybrid solutions between breathers and solitons are constructed by applying the complex conjugate method to multi-soliton solutions. Furthermore, their evolutions are shown graphically by choosing suitable parameters.
- breather wave solutions,
- rouge waves,
- resonant multi-soliton solutions,
- M-breather solutions,
- hybrid solutions
Citation: Sixing Tao. Breather wave, resonant multi-soliton and M-breather wave solutions for a (3+1)-dimensional nonlinear evolution equation[J]. AIMS Mathematics, 2022, 7(9): 15795-15811. doi: 10.3934/math.2022864

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Abstract

In this paper, a (3+1)-dimensional nonlinear evolution equation is considered. First, its bilinear formalism is derived by introducing dependent variable transformation. Then, its breather wave solutions are obtained by employing the extend homoclinic test method and related figures are presented to illustrate the dynamical features of these obtained solutions. Next, its resonant multi-soliton solutions are obtained by using the linear superposition principle. Meanwhile, 3D profiles and contour plots are presented to exhibit the process of wave motion. Finally, M-breather wave solutions such as one-breather, two-breather, three-breather and hybrid solutions between breathers and solitons are constructed by applying the complex conjugate method to multi-soliton solutions. Furthermore, their evolutions are shown graphically by choosing suitable parameters.

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