Exact traveling wave solutions and $$L^{1}$$ L 1 stability for the shallow water wave model of moderate amplitude

Abstract

In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in $$L^{1}(R)$$ space for the Cauchy problem of the equation.