Abundant travelling wave solutions of 3+1 dimensional Boussinesq equation with dual dispersion

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

On the Instability of a Class of Periodic Travelling Wave Solutions of the Modified Boussinesq Equation

This paper is concerned with instability of periodic travelling wave solutions of the modified Boussinesq equation. Periodic travelling wave solutions with a fixed fundamental period Lwill be constructed by using Jacobi’s elliptic functions. It will be shown that these solutions, called dnoidal waves, are nonlinearly unstable in the energy space for a range of their speeds of propagation and pe...

Travelling wave solutions to Zufiria’s higher-order Boussinesq type equations

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...

New exact travelling wave solutions for the K(2, 2) equation with osmosis dispersion

In this paper, by using bifurcation method, we successfully find the K(2, 2) equation with osmosis dispersion ut+(u )x− (u)xxx = 0 possess two new types of travelling wave solutions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained....

Traveling solitary wave solutions to the generalized Boussinesq equation

In this paper, we are concerned with the generalized Boussinesq equation including the singularly sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By the means of two proper ansatzs, we obtain explicit traveling solitary wave solutio...