Peaked and Smooth Solitons forK*(4,1)Equation

[摘要] This paper is contributed to explore all possible single peak solutions for theK*(4,1)equationut=uxu2+2α(uuxxx+2uxuxx). Our procedure shows that theK*(4,1)equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestallimξ→±∞u=A≠0or possesses compacton solutions only whenlimξ→±∞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 theK*(4,1)equation.

[学科分类] 应用数学