[PDF] Top 20 Exact Solutions to the Generalized Benjamin Equation

... u + α u u + β u = , (3) where α and β are constants. Equation (3) is used in the analysis of long wave in shallow water; see [28]. To the best of our knowledge, there are a few articles about this equation. ... See full document

... the generalized exp( ϕ ( ξ ) ) -expansion method is used to find traveling wave solutions of Korteweg-de Varies equation (KdV) and modified Liouville ...wave solutions and finally solitary ... See full document

... In this section, we study the traveling wave solutions of the generalized Equal width equation on the premise of finding the exact solution of the Equal width equation. The obtained ... See full document

... (2014) Exact Traveling Wave Solutions of the (3 + 1)-Dimensional mKdV-ZK Equation and the (1 + 1)-Dimensional Compound KdVB Equation Using New Approach of the Generalized ... See full document

... of Equation (6) is well known to us, inserting the values of α i ( i = 0,1, 2,  , N ) , β i ( i = 1, 2,  , N ) , d and V into Equation (4), we obtain more general type and new exact traveling wave ... See full document

... of exact analyt- ical solutions including generalized trigonometric and hyperbolic functions solutions of this equation with the improved fractional Riccati expansion method in ...RLW ... See full document

... (NLS) equation is one of the important mathematical mod- els in many fields of physics, which has been widely applied in Bose-Einstein condensates [–], nonlinear optical fiber communication [, ], plasma physics ... See full document

... In order to explore new analysis solutions to the system 1, we attempted to use the first integral method to solve the generalized Zakharov equation for the first time.. The rest of the [r] ... See full document

... wave solutions for the generalized Camassa-Holm Equation ...Holm equation by using homtopy analysis ...wave solutions of (4) in the form of u x t ( ) , = φ ( x − ct ) = φ ξ ( ) , where ... See full document

... wave solutions are ...trial equation method ...KdV equation and obtained traveling wave solutions; in [33–38] was introduced a method called the G G -expansion method and one obtained a ... See full document

... solutions. These solutions may be useful for describing certain nonlinear physical phenomena of Equation (1.1). The method which we have propose in this paper is standard, direct and computerized ... See full document

... (vi) To determine the parameter M, the linear terms of highest order in the resulting equation with the highest-order nonlinear terms are balanced. With M determined, one collects all the coefficients of powers of Y ... See full document

... smooth solutions and local blow up solutions of the KP ...These solutions can be used to qualitative or numerical analysis for properties of the KP ...the generalized variable separa- tion ... See full document

... wave solutions given by solution (9), different kinds of multi-solitary wave interactions can be figured and ...obtained exact solutions of the BO equation, the propa- gation and interaction ... See full document

... polynomial solutions to the corresponding generalized bilinear equation by Maple symbolic computation and generate four classes of rational solutions to the resulting Shallow Water Wave-like ... See full document

... of exact traveling wave solutions for the generalized sine–Gordon equation by using this binary ...the exact solutions of NLEEs in mathematical ... See full document

... Perhaps the simplest universal equations with algebraic soliton solutions are of the modified Korteweg-de Vries (KdV) type [4]. KdV-type models, for example, underpin Fermi-Pasta-Ulam de- scriptions of lattice ... See full document

... for exact 1-soliton ...retrieve exact soliton ...simplest equation method are recent popular approaches that are going to be implemented in this paper in order to obtain soliton solutions to a ... See full document

... Abstract—The Benjamin-Ono (BO) equation is a nonlinear partial integro-differential equation that describes internal waves in deep stratified ... See full document

... A Lie point symmetry of a differential equation is an invertible trans- formation of the dependent and independent variables that leaves the equation unchanged. Finding all the symmetries of a differential ... See full document