Single Peak Solitons for the Boussinesq-Like B(2,2) Equation

Abstract

The nonlinear dispersive Boussinesq-like B(2,2) equation utt+(u2)xx−(u2)xxxx=0, which exhibits single peak solitons, is investigated. Peakons, cuspons and smooth soliton solutions are obtained by setting the B(2,2) equation under inhomogeneous boundary condition. Asymptotic behavior and numerical simulations are provided for these three types of single peak soliton solutions of the B(2,2) equation.