The classification of travelling wave solutions and superposition of multi-solutions to Camassa-- Holm equation with dispersion |
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Authors: | Liu Cheng-Shi |
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Institution: | Department of Mathematics, Daqing Petroleum Institute, Daqing 163318, China |
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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. |
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Keywords: | classification of
travelling wave solution symmetry group Camassa--Holm equation with dispersion superposition of solutions |
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