Travelling wave solutions in a class of generalized Korteweg–de Vries equation

In this paper, we consider a new generalization of KdV equation ut = uxul−2 + α[2uxxxup + 4pup−1uxuxx + p(p − 1)up− 2(ux)3] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory.