Symmetries and Applications of Differential Equations

This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include:

-- Approximate symmetry in nonlinear physical problems

-- Complex methods for Lie symmetry analysis

-- Lie group classication, Symmetry analysis, and conservation laws

-- Conservative difference schemes

-- Hamiltonian structure and conservation laws of three-dimensional linear elasticity

-- Involutive systems of partial differential equations

This collection of works is written in memory of Professor Nail H. Ibragimov (19392018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.

Presents the recent development of Lie group analysis and applications of differential equations Provides works collected in the memory of Professor Nail H. Ibragimov (1939-2018) Introduces new methods and applications in linear and nonlinear differential equations

Autorentext
Professor Albert C. J. Luo has worked at Southern Illinois University Edwardsville, USA for over 30 years. Dr. Luo is an international well-known scientist in Nonlinear Dynamics and Mechanics.

Professor Rafail K. Gazizov has worked at Ufa State Aviation Technical Universit, Ufa, Russia for almost 40 years. Dr. Gazizov is a recognized, well-known scientist in Differential Equations and Applications.

Inhalt
Approximate symmetry in nonlinear physics problems.- One-dimensional ows of a polytropic gas: Lie group classication, conservation laws, invariant and conservative difference schemes.- Hamiltonian structure and conservation laws of three-dimensional linear elasticity theory.-Complex methods for Lie symmetry analysis.- Symmetry analysis and conservation laws of a family of Boussinesq equations.- Group Analysis of the Guéant and Pu Model of Option Pricing and Hedging.- On Involutive Systems of Partial Differential Equations.- Group analysis of some Camassa-Holm type equations.