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Under the traveling wave transformation, Camassa-Holm equation withdispersion is reduced to an integrable ODE whose general solution can beobtained using the trick of one-parameter group. Furthermore combining completediscrimination system for polynomial, the classifications of all singletraveling wave solutions to the Camassa-Holm equation with dispersion isobtained. In particular, an affine subspace structure in the set of thesolutions of the reduced ODE is obtained. More general, an implicit linearstructure in Camassa-Holm equation with dispersion is found. According to thelinear structure, we obtain the superposition of multi-solutions toCamassa-Holm equation with dispersion

The classification of travelling wave solutions and superposition of multi-solutions to Camassa–Holm equation with dispersion