Exact Solutions of Two Nonlinear Partial Differential Equations by the First Integral Method

New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

and Applied Analysis 3 P(X, Y) = ∑ m i=0 a i (X)Y i is an irreducible polynomial in the complex domain C[X, Y] such that P [X (ξ) , Y (ξ)] = m ∑ i=0 a i (X (ξ)) Y i (ξ) = 0, (13) where a i (X), (i = 0, 1, 2, . . . , m) are polynomials of X and a m (X) ̸ = 0. Equation (13) is called the first integral to (12a) and (12b). Due to the Division Theorem, there exists a polynomial h(X) + g(X)Y in the c...

On the Exact Solution for Nonlinear Partial Differential Equations

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

Exact solutions of nonlinear interval Volterra integral equations

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Exact solutions of nonlinear partial differential equations by singularity analysis

Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool is the appropriate use of the singularities of the solutions, and this can be done without knowing these solutions in advance. Since the elaboration of the si...