B\"acklund transformations for the Camassa-Holm equation
Alexander G. Rasin, Jeremy Schiff
TL;DR
This paper introduces a novel Bäcklund transformation for the Camassa-Holm equation that acts on both dependent and independent variables, enabling new solution constructions and symmetry analyses.
Contribution
It presents a new Bäcklund transformation for the CH equation, including superposition principles and applications to solution generation and symmetry derivation.
Findings
Constructed traveling wave solutions.
Developed a method for multi-soliton and multi-cuspon solutions.
Derived generating functions for symmetries and conservation laws.
Abstract
The B\"acklund 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 multi-soliton, multi-cuspon and soliton-cuspon solutions, and a derivation of generating functions for the local symmetries and conservation laws of the CH hierarchy.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.