The auxiliary equation method for solving the Zakharov–Kuznetsov (ZK) equation

Abstract

a b s t r a c t In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the auxiliary equation method. As a result, new solitary pattern, solitary wave and singular solitary wave solutions are found.

Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

“…, a = e in our results (3.2.11),(3.2.12),(3.2.14) and (3.2.15) we have the wellknown results u 1 , u 2 of (10) and u 1 , u 2 of (13) obtained in [73]. (m,1,1), m 3 In this case Eq.…”

“…The function governs the behaviour of weakly nonlinear ion acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field [77]. Recently, Ma et al [73] This work is concerned with two cases of Eq. (3.2.1):…”

By using a new iterative method to the generalized system Zakharov-Kuznetsov and estimate the best parameters via applied the pso algorithm

“…As shown from (13), it is an equivalent solution (∑ ) to (3), where i = 0,1,2,3 .... are given by ( 8), (10). The R-term Approximate solution of ( 13) is given by ∑ .…”

“…Rowlands and infield method the Zakharov-Kuznetsov system was examined for wave length disorders [9]. Via using the auxiliary equation method was solved Zakharov-Kuznetsov [10]. The solution of Zakharov-Kuznetsov system via variational iteration method with the description of partial derivatives using caputo [11].…”

Localized interaction solutions of the (2+1)-dimensional Ito Equation

“…More and more different types of rational solutions have been found, such as algebraic solitons, lump solutions, rogue wave solutions. Many types of efficient methods have been developed including Bäcklund transformation [18,19], C-K direct method [2,7], Darboux transformation [17], the auxiliary equation method [8], Hirota bilinear approach [3], long wave limit method, inverse scattering approach [1], and so on. However, the Hirota bilinear transformation plays a critical role in finding the lump solution in terms of Pfaffian form solution and N soliton wave solution [12].…”