New exact traveling wave solutions to the (1+1)-dimensional Klein-Gordon-Zakharov equation for wave propagation in plasma using the exp(-Φ(ξ))-expansion method

Abstract

The (1þ1)-dimensional nonlinear Klein-Gordon-Zakharov equation considered as a model equation for describing the interaction of the Langmuir wave and the ion acoustic wave in high frequency plasma. By the execution of the exp(-Φ(ξ))-expansion, we obtain new explicit and exact traveling wave solutions to this equation. The obtained solutions include kink, singular kink, periodic wave solutions, soliton solutions and solitary wave solutions of bell types. The variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in plasma physics and engineering.

Auxiliary equation method for ill-posed Boussinesq equation

“…Recent research for the past few decades contains some well-known methods which have been formulated to get exact soliton solutions of nonlinear physical problems by applying symbolic computation approach with the help of a software such as Maple etc. These methods embody homotopy perturbation method [1], variational iteration method [2], exp-function method [3][4][5][6], homotopy analysis method [7], improved tan 2 f ( ) -expansion method [8,9], trial equation method [10], Tanh method [11][12][13], exponential rational function method [14,15], G G ¢ ( ) -expansion method [16][17][18], modified simple equation method [19,20], Kudryashov method [21,22] and exp h -F ( ( ))-expansion method [23,24] etc.…”