Related papers: A multiple exp-function method for nonlinear diffe…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (2+1)-dimensional variable-coefficient…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincar\'e symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution.…
This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
Exact single-wave and two-wave solutions of systems of equations of Newell-Whitehead type are presented. The Painleve test and calculations in the spirit of Hirota are used to construct these solutions.
We discuss the relation between the modified method of simplest equation and the exp-function method. First on the basis of our experience from the application of the method of simplest equation we generalize the exp-function ansatz. Then…
Complete discrimination system for polynomial and direct integral method were discussed systematically. In particularly, we pointed out some mistaken viewpoints. Combining with complete discrimination system for polynomial, direct integral…
Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained.…
In this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
Multi-soliton solution of the 3-waves problem is represented in explicit determinative form.
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…