Singular traveling wave solutions for Boussinesq equation with power law nonlinearity and dual dispersion

Abstract

Abstract In this paper we study the Boussinesq equation with power law nonlinearity and dual dispersion which arises in fluid dynamics. A particular kind of product of distributions is introduced and applied to solve non-smooth solutions of this equation. It is proved that, under certain conditions, a distribution solution as a singular Dirac delta function exists for this model. For the first time, this kind of product of distributions is used to deal with a fourth order nonlinear partial differential equation.

Keywords

• Boussinesq equation
• Dual dispersion
• Product of distributions
• Traveling delta wave solution