Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint

Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

“…In recent years, quite a few methods for obtaining explicit traveling and solitary wave solutions of nonlinear evolution equations have been proposed. In recent years, exact homoclinic and heteroclinic solutions were proposed for some NEEs like nonlinear Schrödinger equation, Sine-Gordon equation, DaveyStewartson equation, Zakharov equation, and Boussinesq equation [1][2][3][4][5][6][7].…”

Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

“…Very recently, the analytical and numerical solutions of the ill posed Boussinesq equation were examined intensively in the literature. In [36], the authors studied the explicit homoclinic orbits solutions for Equation (2) with periodic boundary condition and even constraint. In [37], Jafari et al obtained the solitary wave solutions of Equation (2) by sine-cosine and extended tanh func-tion method.…”

“…It di ers only in the sign of the last dispersive term of the Equation (2). The Equation (2) is used to describe twodimensional ow of shallow-water waves having small amplitudes [36]. In the weakly nonlinear limit, the shallow water wave equation for long waves reduces to the KdV equation.…”

Exact Multi-soliton Solution for the (3+1)-D Jimbo-Miwa Equation

“…As mathematical models of these phenomena, the investigation of exact solutions is important in mathematical physics. Many methods are available to look for exact solutions of nonlinear evolution equations, such as the inverse scattering method, the Lie group method, the mapping method, Exp-function method, ansätz technique, three-wave tape of ansätz approach and so on (Ma and Fan(2011), Liu et al(2005), Dai et al(2005)). In this paper, we consider the following Jimbo-Miwa equation:…”