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.

In this paper, the topological (dark) as well as non-topological (bright) soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that, it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc...) envelope...

The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the ”long wave limit” procedure of Ablowitz and Satsuma, and appropriate ”gauge” transformations. Their properties are also discussed and it is shown that these solutions interact elastically with...

In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With help of Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on finite difference get numerical one-soliton We graphically show shock-wave solutions, observe that solutions are explosive unsta...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota's bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...

Binary Bargmann symmetry constraints are applied to decompose soliton equations into finite-dimensional Liouville integrable Hamiltonian systems, generated from so-called constrained flows. The resulting constraints on the potentials of soliton equations give rise to involutive solutions to soliton equations, and thus the integrability by quadratures are shown for soliton equations by the const...

In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x = 3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the r...

In this paper many soliton-like solutions with the arbitrary functions of y and t are obtained for the 1+2D Calogero-Bogoyavlenskii-Schif equation by means of some generalized ansatz and symbolic computation. Some new exact solutions are also presented from the obtained soliton-like solutions. Shock wave solution is only a special case.

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539-541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solution...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...