Abstract Under the travelling wave transformation, the Camassa--Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa--Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa--Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa--Holm equation with dispersion.
Received: 25 September 2006
Revised: 06 November 2006
Accepted manuscript online:
Liu Cheng-Shi(刘成仕) The classification of travelling wave solutions and superposition of multi-solutions to Camassa-- Holm equation with dispersion 2007 Chinese Physics 16 1832
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