Nonlinear evolution wave equations (NEEs) are partial differential equations (PDEs) involving first or second order derivatives with respect to time. Such equations have been intensively studied for the past few decades [1-3] and several new methods to solve nonlinear PDEs either numerically or analytically are now available. Hirota's bilinear method is a powerful tool for obtaining a wide clas...

Partial differential equations (PDEs) are powerful tools for the generation of free-form surfaces. In this paper, techniques of surface representation using PDEs of different orders are investigated. In order to investigate the realtime performance and capacity of surface generation based on the PDE method, the forms of three types of partial differential equations are put forward, which are th...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

• Symmetry analysis of differential equations: classical and nonclassical symmetries, potential symmetries, group–invariant solutions, variational symmetries and conservation laws • Applications of symmetry analysis theory to mathematical models arising in mathematical physics, mathematical biology, image processing, engineering, financial mathematics and other research fields • Geometric appro...

A double sub-equation method is presented for constructing complexiton solutions of nonlinear partial differential equations (PDEs). The main idea of the method is to take full advantage of two solvable ordinary differential equations with different independent variables. With the aid of Maple, one can obtain both complexiton solutions, combining elementary functions and the Jacobi elliptic fun...

In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

A new approach using optimization technique for constructing low-dimensional dynamical systems of nonlinear partial differential equations (PDEs) is presented. After the spatial basis functions of the nonlinear PDEs are chosen, spatial basis functions expansions combined with weighted residual methods are used for time/space separation and truncation to obtain a high-dimensional dynamical syste...

In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs) and present some sufficient conditions for multi-symplecticity of PRK methods of Hamiltonian PDEs.

In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a nontrivial kernel, which allows one to reduce the nonlinear PDEs to systems of non-differential (algebraic or transcendental) equations for the unknown fields. In ...

This article presents the heat and mass transfer characteristics of unsteady MHD flow of a viscous, incompressible and electrically conducting micropolar fluid in the presence of viscous dissipation and radiation over a porous stretching sheet with chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) by applying suitable si...