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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 classification, 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 (1939-2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.
List of contents
Approximate symmetry in nonlinear physics problems.- One-dimensional ows of a polytropic gas: Lie group classification, 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.
About the author
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.
