Peaked and Smooth Solitons for K*(4,1) Equation

Abstract

This paper is contributed to explore all possible single peak solutions for the K*(4,1) equation ut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that the K*(4,1) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal limξ→±∞u=A≠0 or possesses compacton solutions only when limξ→±∞u=A=0. We present a new smooth soliton solution in an explicit form. Mathematical analysis and numeric graphs are provided for those soliton solutions of the K*(4,1) equation.