Exact solutions for nonlinear propagation of slow ion acoustic monotonic double layers and a solitary hole in a semirelativistic plasma

Abstract

A small-amplitude slow ion acoustic monotonic double layer in an unmagnetized plasma consisting of relativistic drifting cold electrons and nonrelativistic drifting thermal ions is investigated. By using the reductive perturbation method, Schamel–Korteweg–de Vries (SKdV) and Schamel equations are derived. We used the linearization transformation to obtained the solutions of the SKdV and Schamel equations. The method is based upon a linearization principle that can be applied on nonlinearities which have a polynomial form. We illustrate the potential of the method by finding solutions of the SKdV and Schamel equations. Furthermore, we show that the monotonic double-layer solution is a nonlinear extension of the slow ion acoustic solitary hole having a negative trapping parameter in a semi relativistic plasma.

Painleve analysis, Auto-Backlund transformation and new exact solutions for improved modied KdV equation

“…By using the linearized transformation [21], we find the solution for the IMKdV equation (1) by substitution of the following:…”

“…Many other methods have been developed, such as the inverse scattering transform [1] Bäcklund transformation method [2][3][4][5][6], Painlevé analysis [7][8], truncated Painlevé analysis [9], bilinear transformation [10], tanh method [11][12], extended homogeneous balance method [13][14][15], extended tanh function method [16][17][18][19][20] and linearized transformation [21][22]. The Bäcklund transformations (BT) of nonlinear partial differential equations (PDEs) play an important role in soliton theory, which is an efficient method to obtain exact solutions of nonlinear PDEs.…”

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

“…The Schamel-KdV equation was also derived for this kind of plasma by reductive perturbation method [29]. Analytic solutions of the equation were obtained by using a linearized principle and the slow ion-acoustic monotonic double layers were suggested in [29]. The body of our paper is structured in the following order: Methods and their detailed structures are given in Section 2.…”

“…The nonlinear behavior of ion-acoustic wave contains lots of detail about the solitary wave solutions in an unmagnetized plasma that is the plasma consisting nonrelativistic drifting ions and relativistic drifting electrons. The Schamel-KdV equation was also derived for this kind of plasma by reductive perturbation method [29]. Analytic solutions of the equation were obtained by using a linearized principle and the slow ion-acoustic monotonic double layers were suggested in [29].…”

Solitary Wave Solution of the Two-Dimensional Regularized Long-Wave and Davey-Stewartson Equations in Fluids and Plasmas

“…To this aim, a vast variety of powerful and direct methods for finding the exact significant solutions of the NLPDEs through it is rather difficult have been derived. Some of the most important methods are Hirota's dependent variable transformation [1], the Bäcklund transformations (BTs) [2], the inverse scattering transformation [3], Painlevé expansions [4], Jacobi elliptic function expansion method [5][6][7], the homogenous balance method [8], the linearized transformation method [9][10][11], the F-expansion method [12,13], Fan-sub-equation method, extended and modified extended Fan-sub equation method [14][15][16][17][18], the tanh-function method and extended tanh-function method [19][20][21], the tanh-sech method [22], the sine-cosine method [23,24], variational iteration method [25], homotopy perturbation method [26], the G G  -expansion method [27][28][29] and several ansatz methods [30][31][32][33][34]. The Frobenius integrable decompositions (FIDs) and rational function transformations (RFTs) are used to construct exact solutions to NLPDEs with BTs and auto BTs [35][36][37][38][39][40].…”