Stumpons are non-conservative traveling waves of the Camassa-Holm equation

被引：2
|
作者：
Galtung, Sondre Tesdal [1 ]
Grunert, Katrin [1 ]
机构：
[1] NTNU Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2022年 / 433卷
关键词：
Camassa-Holm equation; Traveling wave solutions; Conservative solutions; Energy-preserving numerical methods; GLOBAL CONSERVATIVE SOLUTIONS; SHALLOW-WATER EQUATION; DISSIPATIVE SOLUTIONS; GEODESIC-FLOW; INITIAL DATA; STABILITY;
D O I：
10.1016/j.physd.2022.133196
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well-known that by requiring solutions of the Camassa-Holm equation to satisfy a particular local conservation law for the energy in the weak sense, one obtains what is known as conservative solutions. As conservative solutions preserve energy, one might be inclined to think that any solitary traveling wave is conservative. However, in this paper we prove that this is not true for the traveling waves known as stumpons. We illustrate this result by comparing the stumpon to simulations produced by a recently developed numerical scheme for conservative solutions. (C) 2022 The Author(s). Published by Elsevier B.V.
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页数：17
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