Lump chains in the KP‐I equation

Lester, Charles; Gelash, Andrey; Zakharov, Dmitry; Захаров, В. Е.

doi:10.1111/sapm.12420

Cited by 47 publications

(14 citation statements)

References 40 publications

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“…It should be noted that the resonant interaction between a breather and a line soliton involves a resonant line soliton which is different from the original line soliton, so we analyze the asymptotic properties of a breather and two line solitons. From the resonant solution (32), we obtain the line soliton named as line soliton 2 moves along 2ξ 1 − ξ 2 ≈ 0. The line soliton 2 can be expressed as follows:…”

Section: Resonant Interactions Between a Breather And A Line Solitonmentioning

confidence: 99%

“…[31] Although the multi-line solitons of the KP-I equation can not realize the resonant interaction, the breathers of the KP-I equation can form the web-shaped waveforms. [32] Johnson and Thompson gave a resonant solution of a lump and a line soliton for KP-I equation. [33] During the partial resonant interaction between a lump and a line soliton, the lump exhibits two different dynamical behaviors.…”

Section: Introductionmentioning

confidence: 99%

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Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

2023

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The (2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semi-discrete Kadomtsev-Petviashvili I equation. This paper focuses on investigating the resonant interactions between two breathers, a breather/lump and line solitons as well as lump molecules for the (2+1)-dimensional elliptic Toda equation. Based on the N-soliton solution, we obtain the hybrid solutions consisting of line solitons, breathers and lumps. Through the asymptotic analysis of these hybrid solutions, we derive the phase shifts of the breather, lump and line solitons before and after the interaction between a breather/lump and line solitons. By making the phase shifts infinite, we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons. Through the asymptotic analysis of these resonant solutions, we demonstrate the resonant interactions exhibit the fusion, fission, time-localized breather and rogue lump phenomena. Utilizing the velocity resonance method, we obtain lump-soliton, lump-breather, lump-soliton-breather and lump-breather-breather molecules. The above works have not been reported in the (2+1)-dimensional discrete nonlinear wave equations.

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Section: Resonant Interactions Between a Breather And A Line Solitonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

2023

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“…The reports on anomalous scattering focus on the diversity of scattering patterns, such as triangular patterns, and polygonal patterns [17]. At the same time, the resonance phenomenon between lump chains (we called breather waves in this paper) and lump waves has been fully studied [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation

Wang

Chen

2022

Advances in Mathematical Physics

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Most of the papers have explored the interactions between solitons with a zero background, while reports about exact solutions for nonzero background are rare. Hence, this paper is aimed at exploring the breather, lump, and interaction solutions with a small perturbation to ( 2 + 1 )-dimensional generalized Kadomtsev-Petviashvili (gKP) equation. General high-order periodic breather solutions are obtained using Hirota’s bilinear method with a small perturbation. At the same time, combining the use of long wave limit methods and module resonance constraints, general lump solutions and mixed solutions to gKP equation are generated. Finally, the space-time structures of the breather solutions, lump solutions, and interaction solutions are investigated and discussed.

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“…and ϑ jk is a constant M × M matrix. The lump chains of the KPI equation have been constructed by means of the reduction version of the Gramian form of the τ-function [27].…”

Section: Introductionmentioning

confidence: 99%

Multiple lump molecules and interaction solutions of the Kadomtsev–Petviashvili I equation

Zhao¹,

He²

2022

Commun. Theor. Phys.

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In this paper, a modified version of the solution in form of Grammian formula is employed to investigate a new type of multiple lump molecule solution of the Kadomtsev-Petviashvili I equation. The high-order multiple lump molecules consisting of M N-lump molecules are constructed by means of the Mth-order determinant and the non-homogeneous polynomial in the degree of 2N. The interaction solutions describing P line solitons radiating P of the M N-lump molecules are constructed. The dynamic behaviors of some specific solutions are analyzed through numerical simulation. All the results will enrich our understanding about the multiple lump waves of the Kadomtsev-Petviashvili I equation.

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Lump chains in the KP‐I equation

Cited by 47 publications

References 40 publications

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the (2+1)-dimensional elliptic Toda equation

Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation

Multiple lump molecules and interaction solutions of the Kadomtsev–Petviashvili I equation

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