Nonlinear delay reaction–diffusion equations with varying transfer coefficients: Exact methods and new solutions

New Exact Solutions for Two Nonlinear Equations

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutio...

Exact solutions of nonlinear interval Volterra integral equations

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Similarity transformations for Nonlinear Schrödinger Equations with time varying coefficients : Exact results

In this paper we use a similarity transformation connecting some families of Nonlinear Schrödinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrödinger equation. This transformation allows one to apply all known results for that equation to the original non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, us...

A new method for constructing exact solutions to nonlinear delay partial differential equations

We propose a new method for constructing exact solutions to nonlinear delay reaction–diffusion equations of the form ut = kuxx + F (u,w), where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = ∑N n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or fun...