Novel soliton molecules and wave interactions for a (3 + 1)-dimensional nonlinear evolution equation

Tang, Xiaoyan; Cui, Chao Jie; Liang, Zu feng; Ding, Wei

doi:10.1007/s11071-021-06687-7

Cited by 12 publications

(5 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, some other types of localized excitations, such as instantons, ring solitons, chaotic and fractal patterns are analyzed by selecting the corresponding arbitrary functions. By combining the velocity resonance mechanism, dromion molecules of the (3+1)-dimensional nonlinear systems are discussed [33,34]. Folded solitary waves and the corresponding superimposed structures of an extended (3+1)-dimensional KP-Boussinesq equation are systematically studied by exploring suitable multi-valued functions [35].…”

Section: Discussionmentioning

confidence: 99%

Some Novel Fusion and Fission Phenomena for an Extended (2+1)-Dimensional Shallow Water Wave Equation

Zhou,

Zhu,

Ren

2024

Symmetry

View full text Add to dashboard Cite

An extended (2+1)-dimensional shallow water wave (SWW) model which can describe the evolution of nonlinear shallow water wave propagation in two spatial and temporal coordinates, is systematically studied. The multi-linear variable separation approach is addressed to the extended (2+1)-dimensional SWW equation. The variable separation solution consisting of two arbitrary functions is obtained, by assumption, from a specific ansatz. By selecting these two arbitrary functions as the exponential and trigonometric forms, resonant dromion, lump, and solitoff solutions are derived. Meanwhile, some novel fission and fusion phenomena including the semifoldons, peakons, lump, dromions, and periodic waves are studied with graphical and analytical methods. The results can be used to enhance the variety of the dynamics of the nonlinear wave fields related by engineering and mathematical physics.

show abstract

Section: Discussionmentioning

confidence: 99%

Some Novel Fusion and Fission Phenomena for an Extended (2+1)-Dimensional Shallow Water Wave Equation

Zhou,

Zhu,

Ren

2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…Elastic, inelastic and completely inelastic interaction between two dromions 3.1. Dynamic characteristics of a single dromion structure The exponentially localized dromion structure is an important nonlinear excitation in high dimensions [40][41][42][43][44][45].…”

Section: Variable Seperation Solutionmentioning

confidence: 99%

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

Wang,

Yang,

Tang

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this study, we extend the generalized multilinear variable separation approach to a fifth-order nonlinear evolution equation. By performing asymptotic analysis on the variable separation solution, which is composed of three lower-dimensional functions, we identify a resonant regime governing dromion-dromion/solitoff interactions. In the case of two-dromion interactions, elastic, inelastic, and completely inelastic collisions are possible, while for the dromion-solitoff interaction only inelastic and completely inelastic collisions are permitted. Furthermore, we derive two types of semi-rational solutions from the quadratic function ansatz. In particular, in the scenario of a completely resonant collision between a lump and a line-soliton pair, the lump separates from one line soliton and exists briefly before merging with the other soliton, forming a localized lump in both time and space dimensions. The fusion or fission phenomena between the dromion-dromion/solitoff interaction and the lump-line soliton interaction are shown graphically.

show abstract

“…In [49], some rogue wave solutions are obtained via the Hirota bilinear method. In [50], the lump lattice and ring soliton lattice are constructed. Hereby, we will explore some new solutions, namely, the non-singular complexiton, singular complexiton, and complex multiple soliton solutions to Equation (1.1).…”

Section: Introductionmentioning

confidence: 99%

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Wang,

Shi,

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

This research mainly concerned with some new solutions of the (3 + 1)‐dimensional nonlinear evolution equation (NEE). First, we extract the resonant multiple soliton solutions (RMSSs) by taking advantage of the linear superposition principle (LSP) and weight algorithm (WA). Then the non‐singular complexiton and singular complexiton solutions are developed by introducing pairs of the conjugate parameters. Besides, the complex multiple‐soliton solutions are also explored with the aid of the bilinear approach. The graph descriptions of the attained solutions are paraded to show the dynamical properties. The outcomes of this work are all new and are desirous to bring some new perspective to the investigation of the complexiton solutions to the other partial differential equations (PDEs).

show abstract

Novel soliton molecules and wave interactions for a (3 + 1)-dimensional nonlinear evolution equation

Cited by 12 publications

References 39 publications

Some Novel Fusion and Fission Phenomena for an Extended (2+1)-Dimensional Shallow Water Wave Equation

Some Novel Fusion and Fission Phenomena for an Extended (2+1)-Dimensional Shallow Water Wave Equation

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

Non‐singular complexiton, singular complexiton and complex multiple soliton solutions to the (3 + 1)‐dimensional nonlinear evolution equation

Contact Info

Product

Resources

About