Exact parametric solutions for the first Painlevé nonlinear ODE

Exact First-order Solutions of the Nonlinear Schrodinger Equation

A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~dinger e...

Painlevé test and the first Painlevé hierarchy

Starting from the first Painlevé equation, Painlevé type equations of higher order are obtained by using the singular point analysis.

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Exact solutions of nonlinear interval Volterra integral equations

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...