We develop an inverse scattering transform formalism for the good Boussinesq equation on line. Assuming that solution exists, we show it can be expressed in terms of a $3 \times 3$ matrix Riemann-Hilbert problem. The problem is formulated two reflection coefficients whose definitions involve only initial data, and has form which makes suitable evaluation long-time asymptotics via Deift-Zhou ste...

In this paper, the reduced differential transform method (RDTM) is applied to various nonlinear evolution equations, Korteweg–de Vries Burgers' (KdVB) equation, Drinefel’d–Sokolov–Wilson equations, coupled Burgers equations and modified Boussinesq equation. Approximate solutions obtained by the RDTM are compared with the exact solutions. The present results are in good agreement with the exact ...

(2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation are investigated by employing Jacobi elliptic function expansion method in this paper. As a result, some new forms traveling wave solutions of the equation are reported. Numerical simulation results are shown. These new solutions may be important for the explanation of some practical physical problems. The results of this paper ...