Symmetries of Integro-Differential Equations

This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.

The first monograph to study symmetries of integro-differential, stochastic and delay equations in a unified manner Includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis Offers an accessible presentation and instructive examples Includes supplementary material: sn.pub/extras

Inhalt
to Group Analysis of Differential Equations.- to Group Analysis and Invariant Solutions of Integro-Differential Equations.- The Boltzmann Kinetic Equation and Various Models.- Plasma Kinetic Theory: VlasovMaxwell and Related Equations.- Symmetries of Stochastic Differential Equations.- Delay Differential Equations.