On a matrix KdV6 equation

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-12 DOI:10.1016/j.cnsns.2025.108605

Pilar R. Gordoa , Andrew Pickering , Jonathan A.D. Wattis

引用次数: 0

Abstract

The so-called KdV6 equation has, since its discovery, been the subject of much interest. In this paper we present a matrix version of this equation. On the one hand, we use the Darboux transformation to derive its Bäcklund transformation and a nonlinear superposition formula. These are then used, in the case of upper-triangular matrices, to obtain one- and two-soliton solutions. We find that wave components can combine to produce rogue waves. On the other hand, we derive a second matrix partial differential equation, for which we give auto-Bäcklund transformations of a different kind, similar to those usually given for Painlevé equations.

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在矩阵KdV6方程上

所谓的 KdV6 方程自发现以来一直备受关注。在本文中，我们提出了该方程的矩阵版本。一方面，我们利用达尔布变换推导出其贝克兰变换和非线性叠加公式。然后，在上三角矩阵的情况下，利用这些公式求得单孑子和双孑子解。我们发现，波的成分可以结合起来产生流氓波。另一方面，我们推导出了第二个矩阵偏微分方程，并给出了不同类型的自动贝克隆变换，类似于通常针对潘列维方程给出的自动贝克隆变换。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.