An Integrable Two-Component Degasperis–Procesi Equation

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-03-25 DOI:10.1111/sapm.70045

Nianhua Li, Bao-Feng Feng

引用次数: 0

Abstract

We propose a new two-component Degasperis–Procesi (2-DP) equation, which is shown to be integrable. First of all, we derive an integrable three-component system from the Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) associativity equation and construct its Lax pair and bi-Hamiltonian structure. Next, a 2-DP equation is proposed as further reduction of this three-component system, along with its Lax pair and associated bi-Hamiltonian structure. A reciprocal transformation is found to connect the 2-DP equation with a negative flow in a coupled KdV hierarchy, the associated system has the property of Painlevé. Finally, infinitely many conserved quantities, simple periodic and soliton solutions for the newly integrable 2-DP equation are provided.

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可积分双分量德加斯佩里斯-普罗塞西方程

我们提出了一个新的两分量德加斯佩里斯-普罗切斯（2-DP）方程，并证明它是可积分的。首先，我们从维特-迪克格拉夫-韦林德-韦林德（Witten-Dijkgraaf-Verlinde-Verlinde，WDVV）关联方程推导出一个可积分的三分量系统，并构建了它的拉克斯对和双哈密顿结构。接下来，我们提出了一个 2-DP 方程，作为该三分量系统的进一步还原，以及其 Lax 对和相关的双哈密顿结构。我们发现了一种倒易变换，可以将 2-DP 方程与耦合 KdV 层次中的负流连接起来，相关系统具有 Painlevé 特性。最后，为新的可积分 2-DP 方程提供了无穷多个守恒量、简单周期解和孤子解。

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

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.