695 citations · 1.8k across the 51 of their papers we have counts for
5 papers · 1 filter
Quasi-exact solutions of nonlinear differential equations
Nikolay A. Kudryashov, Mark B. Kochanov
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters…
Analytical properties and exact solutions of the Lotka--Volterra competition system
Nikolay A. Kudryashov, Anastasia S. Zakharchenko
The Lotka--Volterra competition system with diffusion is considered. The Painlevé property of this system is investigated. Exact traveling wave solutions of the Lotka--Volterra com…
Logistic function as solution of many nonlinear differential equations
Nikolai A. Kudryashov, Mikhail A. Chmykhov
The logistic function is shown to be solution of the Riccati equation, some second-order nonlinear ordinary differential equations and many third-order nonlinear ordinary different…
Analytical and numerical studying of the perturbed Korteweg--de Vries equation
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
The perturbed Korteweg--de Vries equation is considered. This equation is used for the description of one--dimensional viscous gas dynamics, nonlinear waves in a liquid with gas bu…
Multi-particle dynamical systems and polynomials
Maria V. Demina, Nikolai A. Kudryashov
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding p…