Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics

✍ Scribed by Victor A Galaktionov; Sergey R Svirshchevskii

• Publisher: Chapman & Hall/CRC
• Year: 2007
• Tongue: English
• Leaves: 530
• Series: Chapman & Hall/CRC applied mathematics and nonlinear science series
• Category: Library

✦ Synopsis

"Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators."--BOOK JACKET. Read more... Content: Introduction : nonlinear partial differential equations and exact solutions -- 1. Linear invariant subspaces in quasilinear equations : basic examples and models -- 2. Invariant subspaces and modules : mathematics in one dimension -- 3. Parabolic equations in one dimension : thin film, Kuramoto-Sivashinsky, and magma models -- 4. Odd-order one-dimensional equations : Korteweg-de Vries, compaction, nonlinear dispersion, and Harry Dym models -- 5. Quasilinear wave and Boussinesq models in one dimension. Systems of nonlinear equations -- 6. Applications to nonlinear partial differential equations in IR[superscript N] -- 7. Partially invariant subspaces, invariant sets, and generalized separation of variables Abstract: Presents examples of interesting solutions on linear invariant subspaces for nonlinear operators. This book develops several techniques for constructing exact solutions that describe singularity behavior for various nonlinear PDEs, including gas dynamics models, free-boundary problems, and Green-Naghdi equations. Read more...

✦ Table of Contents

Front cover......Page 1
Contents......Page 8
Introduction: Nonlinear Partial Differential Equations and Exact Solutions......Page 12
CHAPTER 1. Linear Invariant Subspaces in Quasilinear Equations: Basic Examples and Models......Page 32
CHAPTER 2. Invariant Subspaces and Modules: Mathematics in One Dimension......Page 80
CHAPTER 3. Parabolic Equations in One Dimension: Thin Film, Kuramoto-Sivashinsky, and Magma Models......Page 128
CHAPTER 4. Odd-Order One-Dimensional Equations: Kortweg-de Vries, Compacton, Nonlinear Dispersion, and Harry Dym Models......Page 194
CHAPTER 5. Quasilinear Wave and Boussinesq Models in One Dimension. Systems of Nonlinear Equations......Page 266
CHAPTER 6. Applications to Nonlinear Partial Differential Equations in IR......Page 306
CHAPTER 7. Partially Invariant Subspaces, Invariant Sets, and Generalized Separation of Variables......Page 368
CHAPTER 8. Sign-Invariants for Second-Order Parabolic Equations and Exact Solutions......Page 416
CHAPTER 9. Invariant Subspaces for Discrete Operators, Moving Mesh Methods, and Lattices......Page 460
References......Page 498
List of Frequently Used Abbreviations......Page 524
Index......Page 525
Back cover......Page 530