Peaked and smooth solitons for \(K^*(4,1)\) equation
Summary: This paper is contributed to explore all possible single peak solutions for the \(K^*(4,1)\) equation \(u_t=u_xu^2+2\alpha(uu_{xxx}+2u_xu_{xx})\). Our procedure shows that the \(K^*(4,1)\) equation either has peakon, cuspon, and smooth soliton solutions when sitting on a nonzero constant pedestal \(\lim_{\xi\to\pm\infty}u=A\neq0\) or possesses compacton solutions only when \(\lim_{\xi\to\pm\infty}u=A=0\). 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.
scientific article; zbMATH DE number 6950723