The Peaked And Periodic Peaked Traveling Wave Solutions For A Generalized Camassa-holm Type Equation

The nonlinear partial diferential equation (NPDE) is one of the important aspects inthe contemporary study of nonlinear science, it is a difcult but very important subjectfor solving partial diferential equation. Many powerful and efcient methods to constructexact solutions of nonlinear partial diferential equations have been established and developedby a diverse group of scientists, such as the Ba¨cklund transformation, the inverse scatteringtransform, the Darboux transformation, the direct reduction method, Hirota bilinear method,the classical and non classical Lie group approaches, variable separation method, Painleve′expansion method, sub-equation expansion method and so on.And in this article, one of important properties of the Camassa-Holm equation, themodified Camassa-Holm equation, the Degasperis-Procesi equation and Novikov equation isthe existence of the peaked traveling wave and periodic peaked traveling wave solutions. Inthis article, a generalized Camassa-Holm type equation is introduced. It is shown that thisnonlinear dispersive equation admits the peaked traveling wave solutions and periodic peakedtraveling wave solutions.