Investigation of multi-soliton, multi-cuspon solutions to the Camassa-Holm equation and their interaction

Abstract

The authors study the multi-soliton, multi-cuspon solutions to the Camassa-Holm equation and their interaction. According to the solution formula due to Li in 2004 and 2005, the authors give the proper choice of parameters for multi-soliton and multicuspon solutions, especially for n ≥ 3 case. The numerical method (the so-called local discontinuous Galerkin (LDG) method) is also used to simulate the solutions and give the comparison of exact solutions and numerical solutions. The numerical results for the two-soliton and one-cuspon, one-soliton and two-cuspon, three-soliton, three-cuspon, three-soliton and one-cuspon, two-soliton and two-cuspon, one-soliton and three-cuspon, four-soliton and four-cuspon are investigated by the numerical method for the first time, respectively.

Keywords

Camassa-Holm equation / Local discontinuous Galerkin method / Multisoliton / Multi-cuspon

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