On Compact and Noncompact Structures for the Improved Boussinesq Water Equations

Abstract

The nonlinear variants of the generalized Boussinesq water equations with positive and negative exponents are studied in this paper. The analytic expressions of the compactons, solitons, solitary patterns, and periodic solutions for the equations are obtained by using a technique based on the reduction of order of differential equations. It is shown that the nonlinear variants, or nonlinear variants together with the wave numbers, directly lead to the qualitative change in the physical structures of the solutions.