Symmetries of Integro-Differential Equations: With Applications in Mechanics and Plasma Physics (Lecture Notes in Physics, Vol. 806) (Lecture Notes in Physics (806))

Annotation 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 Front Matter....Pages I-XIII Introduction to Group Analysis of Differential Equations....Pages 1-55 Introduction to Group Analysis and Invariant Solutions of Integro-Differential Equations....Pages 57-111 The Boltzmann Kinetic Equation and Various Models....Pages 113-144 Plasma Kinetic Theory: Vlasov–Maxwell and Related Equations....Pages 145-208 Symmetries of Stochastic Differential Equations....Pages 209-250 Delay Differential Equations....Pages 251-292 Back Matter....Pages 293-305 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.