Bäcklund Transformations for the Camassa–Holm Equation
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- 作者：Alexander G. Rasin ; Jeremy Schiff
- 关键词：Bäcklund transformations ; Camassa ; Holm equation ; Superposition principle ; Wave solutions ; Symmetries ; Conservation laws
- 刊名：Journal of Nonlinear Science
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：27
- 期：1
- 页码：45-69
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Analysis; Theoretical, Mathematical and Computational Physics; Classical Mechanics; Appl.Mathematics/Computational Methods of Engineering; Economic Theory/Quantitative Economics/Mathematical Methods;
- 出版者：Springer US
- ISSN：1432-1467
- 卷排序：27
文摘
The Bäcklund transformation (BT) for the Camassa–Holm (CH) equation is presented and discussed. Unlike the vast majority of BTs studied in the past, for CH the transformation acts on both the dependent and (one of) the independent variables. Superposition principles are given for the action of double BTs on the variables of the CH and the potential CH equations. Applications of the BT and its superposition principles are presented, specifically the construction of travelling wave solutions, a new method to construct multisoliton, multicuspon and soliton–cuspon solutions, and a derivation of generating functions for the local symmetries and conservation laws of the CH hierarchy.