New exact traveling wave solutions for the two-dimensional KdV–Burgers and Boussinesq equations

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

“…Since the Lie point symmetry approach is considered as one of the most powerful technique, we are here interested to use such technique for obtaining the similarity solutions of GKP equation. Generally, this technique is, however, based on the study of the invariance property of the differential equations under one-parameter Lie group of point transformations [13,14]. Since we restrict ourselves to Lie point symmetries, the Lie algebra of the symmetry group of GKP Eq.…”

“…2 where s, n, g, u are infinitesimal transformations of Lie group variables (independent and dependent variables) that have to be determined later. Following the algorithm of Lie [14], we aim to determine the functions s, n, g, u and hence the form of the vector field v. Usually, the determining equations of the functions s, n, g, u are over-determined set of linear partial differential equations. After lengthy calculations and many algebraic manipulations, the set of equations can be solved and yield…”

“…Since the GKP equation can be regarded as universal integrable equation, it is still used as classical model for developing and testing of new mathematical technique. So, a large number of effective mathematical methods have been proposed to solve KP equations [14][15][16][17][18][19][20][21]. Among those, the Lie symmetries are considered as one of the most powerful technique for solving either partial differential equation or nonlinear coupled system of integro-differential equation [22][23][24][25][26][27][28].…”

Application of Extended Tanh Method to Generalized Burgers-type Equations

“…This equation is model equation for wide class of nonlinear wave models of fluid in an elastic tube, liquid with small bubbles and turbulence [14,16,28,30,36]. It has been considered to find out its exact solution by some analytic methods [11,22,35]. In this section, we employ the extended tanh method to find soliton solutions of the generalized two-dimensional Burgers-KdV equation.…”

Explicit exact solutions for the generalized Zakharov equations with nonlinear terms of any order

“…A. Elgarayhi et al [10][11][12] took advantage of the following auxiliary ODE and its solutions dϕ dξ 2 = c 2 ϕ 2 (ξ ) + c 3 ϕ 4 (ξ ) + c 4 ϕ 6 (ξ ), (2) for constructing exact traveling wave solutions of NEEs. But Eqs.…”