The energy method for high-order invariants in shallow water wave equations

被引：6
|
作者：
Zhang, Qifeng [1 ]
Yan, Tong [1 ]
Gao, Guang-hua [2 ]
机构：
[1] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Peoples R China
[2] Nanjing Univ Posts & Telecommun, Dept Math, Nanjing 210023, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2023年 / 142卷
关键词：
Energy method; High -order invariant; Shallow water wave equation;
D O I：
10.1016/j.aml.2023.108626
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Third-order dispersive evolution equations are widely adopted to model one-dimensional long waves and have extensive applications in fluid mechanics, plasma physics and nonlinear optics. The typical representatives are the KdV equation, the Camassa-Holm equation and the Degasperis-Procesi equation. They share many common features such as complete integrability, Lax pairs and bi-Hamiltonian structure. In this paper we revisit high-order invariants for these three types of shallow water wave equations by the energy method in combination of a skew-adjoint operator (1 - partial differential xx)-1. Several applications to seek high-order invariants of the Benjamin-Bona-Mahony equation, the regularized long-wave equation and the Rosenau equation are also presented.(c) 2023 Elsevier Ltd. All rights reserved.
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