Exact Solutions with Jacobi Elliptic Functions of Two Nonlinear Models for Ion-Acoustic Plasma Waves

Abstract

The periodic wave solutions of two nonlinear models for ion-acoustic plasma waves, including the mixed Korteweg-de Vries (KdV) and modified KdV equation and the (3 þ 1)-dimensional modified Zakharov-Kuznetsov equation, are obtained by using the F-expansion method and introducing appropriate transformations. In the limiting cases, the solitary wave solutions of the equations are also obtained.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation

“…It is concluded from these tables that the presented results are more accurate than the results given in [6,36,37]. The approximate solutions ( ) and ( ) of problem (31) From these figures, there is agreement between the approximate and exact solutions.…”

“…It is concluded that the proposed method with all choices of θ and is more accurate than the methods given in [6,36,37]. Consider the following two examples.…”

“…Consider the coupled viscous Burgers' equation: Table 4 compares the results obtained by our method and those given in [6], [36] and [37]. It is concluded from these tables that the presented results are more accurate than the results given in [6,36,37].…”

“…Moreover, the maxi- L ∞ for ( ) Our method for different choice of (θ ) and N=16 (θ ) [36] for N=100 [6] for N=15 [37] (0 0) ( (θ ) [36] for N=100 [6] for N=15 [37] (0 0) ( mum absolute errors are defined by…”

“…A Chebyshev pseudospectral scheme was proposed to approximate the viscous coupled Burgers' equation in [6]. Kaya [7] employed Adomian decomposition scheme to approximate the viscous coupled Burgers' equation.…”