Simple equations method (SEsM): Review and new results

NK Vitanov - AIP Conference Proceedings, 2022 - pubs.aip.org
We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear
partial differential equations. We show that specific case of SEsM can be used in order to …

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

M Saeedian, M Khalighi, N Azimi-Tafreshi, GR Jafari… - Physical Review E, 2017 - APS
Memory has a great impact on the evolution of every process related to human societies.
Among them, the evolution of an epidemic is directly related to the individuals' experiences …

Flows of substances in networks and network channels: Selected results and applications

ZI Dimitrova - Entropy, 2022 - mdpi.com
This review paper is devoted to a brief overview of results and models concerning flows in
networks and channels of networks. First of all, we conduct a survey of the literature in …

Simple equations method (SEsM): Algorithm, connection with Hirota method, inverse scattering transform method, and several other methods

NK Vitanov, ZI Dimitrova, KN Vitanov - Entropy, 2020 - mdpi.com
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact
solutions of nonlinear partial differential equations and to show that several well-known …

Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with …

NK Vitanov, ZI Dimitrova, KN Vitanov - Applied Mathematics and …, 2015 - Elsevier
We discuss the application of a variant of the method of simplest equation for obtaining exact
traveling wave solutions of a class of nonlinear partial differential equations containing …

Simple Equations Method and non-linear differential equations with non-polynomial non-linearity

NK Vitanov, ZI Dimitrova - Entropy, 2021 - mdpi.com
We discuss the application of the Simple Equations Method (SEsM) for obtaining exact
solutions of non-linear differential equations to several cases of equations containing non …

Simple equations method (SEsM) and its particular cases: Hirota method

NK Vitanov, ZI Dimitrova - AIP Conference Proceedings, 2021 - pubs.aip.org
We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear
partial differential equations. We show that the Hirota method is particular case of SEsM for …

Box model of migration channels

NK Vitanov, KN Vitanov - Mathematical Social Sciences, 2016 - Elsevier
We discuss a mathematical model of migration channel based on the truncated Waring
distribution. The truncated Waring distribution is obtained for a more general model of …

The simple equations method (SEsM) for obtaining exact solutions of nonlinear PDEs: Opportunities connected to the exponential functions

NK Vitanov - AIP Conference Proceedings, 2019 - pubs.aip.org
We discuss the last version of a method for obtaining exact solutions of nonlinear partial
differential equations. The method is called the Simple Equations Method (SEsM) and it is …

[HTML][HTML] Traveling waves and statistical distributions connected to systems of interacting populations

NK Vitanov, ZI Dimitrova, KN Vitanov - Computers & Mathematics with …, 2013 - Elsevier
We discuss the following two issues from the dynamics of interacting populations:•(I) density
waves for the case or negligible random fluctuations of the population densities,•(II) …