Nonlinear Reaction-Diffusion Systems

Conditional Symmetry, Exact Solutions and their Applications in Biology

  • Roman Cherniha
  • Vasyl' Davydovych

Part of the Lecture Notes in Mathematics book series (LNM, volume 2196)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Roman Cherniha, Vasyl’ Davydovych
    Pages 45-76
  3. Back Matter
    Pages 155-160

About this book


This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems  and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.


Nonlinear reaction-diffusion system Lie and conditional symmetry Lotka-Volterra system Steady-state solution Q-conditional symmetries of reaction-diffusion systems

Authors and affiliations

  • Roman Cherniha
    • 1
  • Vasyl' Davydovych
    • 2
  1. 1.Institute of MathematicsNational Academy of ScienceKyivUkraine
  2. 2.Institute of MathematicsNational Academy of ScienceKyivUkraine

Bibliographic information