非线性色散 KdV 和 KP 方程的弱紧凑子

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2024-10-22 DOI:10.1111/sapm.12777

S. C. Anco, M. L. Gandarias

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引用次数: 0

摘要

为 K ( m , n ) $K(m,n)$ 方程设计了一种弱公式，它是 gKdV 方程的非线性色散广义化，具有紧凑子解。利用这种表述方法，可以得到明确的弱紧凑子解，包括不存在经典（强）解的弱紧凑子解。类似的结果也适用于 gKP 方程在二维的非线性色散广义化，它具有线紧凑子解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Weak compactons of nonlinearly dispersive KdV and KP equations

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Weak compactons of nonlinearly dispersive KdV and KP equations

A weak formulation is devised for the $K (m, n)$ equation, which is a nonlinearly dispersive generalization of the gKdV equation having compacton solutions. With this formulation, explicit weak compacton solutions are derived, including ones that do not exist as classical (strong) solutions. Similar results are obtained for a nonlinearly dispersive generalization of the gKP equation in two dimensions, which possesses line compacton solutions.

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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.