Abstract
We investigate two interesting (1+1)-dimensional nonlinear partial differential evolution equations (NLPDEEs), namely the nonlinear dispersion equation with compact structures and the generalized Camassa–Holm (CH) equation describing the propagation of unidirectional shallow water waves on a flat bottom, and arising in the study of a certain non-Newtonian fluid. Using an interesting technique known as the sine-cosine method for investigating travelling wave solutions to NLPDEEs, we construct many new families of wave solutions to the previous NLPDEEs, amongst which the periodic waves, enriching the wide class of solutions to the above equations.
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