By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional soliton equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional soliton equation are successfully obtained. The computation for the method appears to be easier and faster by general mathematical software.

The three-soliton solutions to the sine-Gordon equation describing the collision of a kink with a breather or with a kink–antikink pair are given and several separatrix three-soliton solutions are extracted from these solutions. The influence of a small perturbation on the threesoliton collisions is studied numerically. As the perturbed system the Frenkel–Kontorova model with a small degree of ...

A series of new soliton solutions is presented for the inhomogeneous variable coefficient Hirota equation by using Riemann–Hilbert method and transformation relationship. Firstly, through a standard dressing procedure, N-soliton matrix associated with simple zeros in problem constructed. Then can be obtained special relationship from equation. Next, generalized Darboux transformation, high-orde...

This paper is concerned with a lattice model which is suited to square-rectangle transformations characterized by two strain components. The microscopic model involves nonlinear and competing interactions, which play a key role in the stability of soliton solutions and emerge from interactions as a function of particle pairs and noncentral type or bending forces. Special attention is devoted to...

ABSTRACT In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. MATHEMATICS SUBJECT CLASSIFICATION 35 K9...