Solitary wave solutions of two-dimensional nonlinear Kadomtseva€“Petviashvili dynamic equation in dust-acoustic plasmas

摘要

Nonlinear two-dimensional Kadomtseva€“Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing secha€“tanh, sinha€“cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.