Exact Solutions to a Class of Schamel Nonlinear Equations Modeling Dust Ion-acoustic Waves in Plasma

Abstract

In this paper, we apply the extended Kudryashov method to construct some new exact solitary wave solutions of three important physical models, Schamel-nonlinear Schrödinger (S-NLS) equation, Schamel Korteweg-de Vries (S-KdV) equation, Schamel Korteweg-de Vries Burgers (S-KdVB) equation. In addition, this method is applied to seek solutions of Schamel equation modeling ion-acoustic waves in plasma and dust plasma. With the aid of symbolic computation, explicit exact solutions of these equations are expressed in terms of the hyperbolic functions, the trigonometric functions, and the exponential function. The stability of some exact solutions is computationally studied.

Exact Solution, Symmetry Group and Conservation laws for Some (2+1)-dimensional Nonlinear Physical Models

“…The investigation of the exact solutions is an important to provide better information about the mechanism and the applications of NLEEs. Abundant methods are extensively studied to obtain exact solutions, for example the Bäcklund transform [1,2], the extended tanh-function method [3], the F-expansion method [4], sine-cosine method [5], the extended F-expansion method [6], Jacobi elliptic function method [7], the Kudryashov method [8], the extended Kudryashov method [9,10], the Bernoulli sub-equation function method [11], the lie point symmetry method [12]- [14] and other methods [15]- [18].…”