In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has...

In this paper, using the technique of measure of noncompactness in Banach algebra, we prove an existence theorem for a nonlinear integral equation which contains as particular cases a lot of integral and functional-integral equations considered in nonlinear analysis and its applications. Our claim is also illustrated with the applications to some nonlinear functional-integral equation for provi...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

We propose a new method, called the textit{the weighted space method}, for the study of the generalized Hyers-Ulam-Rassias stability. We use this method for a nonlinear functional equation, for Volterra and Fredholm integral operators.

A nonlinear boundary value problem for Laplace's equation is solved numerically by using a reformulation as a nonlinear boundary integral equation. Two numerical methods are proposed and analyzed for discretizing the integral equation, both using product integration to approximate the singular integrals in the equation. The first method uses the product Simpson's rule, and the second is based o...