126 citations · 433 across the 47 of their papers we have counts for
47 papers
On the Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations
Nikolay K. Vitanov
In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (w…
On the mathematical theory of news waves
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
We discuss the spread of a piece of news in a population. This is modeled by SIR model of epidemic spread. The model can be reduced to a nonlinear differential equation for the num…
Probability distribution connected to stationary flow of substance in a channel of network containing finite number of arms
Roumen Borisov, Zlatinka I. Dimitrova, Nikolay K. Vitanov
We discuss a channel consisting of nodes of a network and lines which connect these nodes and form ways for motion of a substance through the channel. We study stationary flow of s…
The Simple Equations Method (SEsM) and the use of exponential functions for obtaining simple and multisoliton solutions of some nonlinear partial differential equations
Nikolay K. Vitanov
We discuss the last version as well as applications of a method for obtaining exact solutions of nonlinear partial differential equations. As this version is based on more than one…
Simple equations method (SEsM) and some of its numerous particular cases
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method i…
Simple Equations methodology (SEsM) for searching of multisolitons and other exact solutions of nonlinear partial differential equations
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a version the methodology for obtaining exact solutions of nonlinear partial differential equations based on the possibility for use of: (i) more than one simplest equat…