Nonlinear partial differential equations (NPDEs) are widely used to describe complex phenomena in various fields of science [...]

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this me...

We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV equation to other NPDEs. The method is based upon a linearization principle which can be applied on nonlinearities which have a polynomial form. We illustrate the ...

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is eff...

ABSTRACT Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modif...

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equa...

in this paper lie’s formalism is applied to deduce classes of solutions of a nonlinear partialdifferential equation (npde) of second order with quadratic nonlinearity. the equation has themeaning of a field equation appearing in the formulation of kinetic models. similaritysolutions and transformations are given in a most general form derived to the first time interms of reciprocal jacobian ell...

Traveling wave solutions of the Oskolkov equation, which is a model describing dynamics an 
 incompressible visco-elastic Kelvin-Voigt fluid, are investigated in this study. Complex trigonometric and complex hyperbolic equation obtained using sub method. In these solutions, graphs presented by assigning special values to parameters. The graphics drawn with computer package program. Impleme...

In this paper a new algebraic procedure is introduced to compute new classes of solutions of (1+1)-nonlinear partial differential equations (nPDEs) of scientific and technical relevance. The crucial step of the method is the basic assumption that the unknown solution of the nPDE under consideration satisfies an ordinary differential equation (ODE) of the first order that can be integrated compl...

A reaction-diffusion stereo algorithm consists of multi-sets of reaction-diffusion equations. Since the equations are described with time-evolving partialdifferential equations, they require much computation time. In addition, the previous algorithm does not state any criterion for convergence judgement; we need to compute the equations for enough duration of time until their solutions converge...