Construction of degenerate lump solutions for (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

Li, Wentao; Li, Biao

doi:10.1016/j.chaos.2024.114572

Cited by 10 publications

(2 citation statements)

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“…Recent research demonstrates that the derivation of lump solutions is achievable through the quadratic functions ansatz, as illustrated by the Kadomtsev-Petviashvili (KP) equation [23][24][25]. Subsequently, these findings have prompted a comprehensive exploration of lump excitations and interaction solutions between lumps and other types of nonlinear waves [26][27][28][29][30]. For example, Hossen obtained three types of interaction solutions to a (3+1)-dimensional model, including the lump-kink wave solution, breathers, and a new interaction solution among the lumps, kink waves and periodic waves [29].…”

Section: Introductionmentioning

confidence: 99%

“…For example, Hossen obtained three types of interaction solutions to a (3+1)-dimensional model, including the lump-kink wave solution, breathers, and a new interaction solution among the lumps, kink waves and periodic waves [29]. Li constructed degenerate lump solutions for the Yu-Toda-Sasa-Fukuyama equation using Hirota's bilinear method and a novel limit approach [30]. Further study suggests that interactions between a lump and a line-soliton pair could lead to the creation of rogue waves [31,32].…”

Section: Introductionmentioning

confidence: 99%

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

Wang,

Yang,

Tang

et al. 2024

Phys. Scr.

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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.

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