Many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed. One of the newest analytical methods to solve nonlinear equations is Reconstruction of variational Iteration Method (RVIM) which is an accurate and a rapid convergence method in finding the approximate solution fo...

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...

In this paper, a method based on Chebyshev polynomials is developed for examination of geometrically nonlinear behaviour of thin rectangular composite laminated plates under end-shortening strain. Different boundary conditions and lay-up configurations are investigated and classical laminated plate theory is used for developing the equilibrium equations. The equilibrium equations are solved dir...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...

In this paper, we apply the Laplace decomposition method to obtain a series solutions of the Burgers-Huxley and Burgers-Fisher equations. The technique is based on the application of Laplace transform to nonlinear partial differential equations. The method does not need linearization, weak nonlinearity assumptions or perturbation theory and the nonlinear terms can be easily handled by using the...

This paper proposes a three-step method for solving nonlinear Volterra integralequations system. The proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear Volterra integral equations system. To showthe advantages of our method some numerical examples are presented.

This article analyzes a strongly nonlinear oscillator with cubic and harmonic restoring force and proposes an efficient analytical technique based on the modified energy balance method (MEBM). The proposed method incorporates higher-order approximations. After applying the proposed MEBM, a set of complicated higher-order nonlinear algebraic equations are obtained. Higher-order nonlinear algebra...