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Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics
1 online resource (xxx, 498 pages) : illustrations
Providing exact solutions of more than 100 nonlinear equations and models, this book begins with classical as well as more recent examples of interesting solutions on linear invariant subspaces for nonlinear operators. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including gas dynamics models, free-boundary problems, Green-Naghdi equations, and quasilinear pseudo-parabolic (magma) equations. Using exact solutions, they describe the evolution properties related to singularity blow-up or extinction phenomena, fin.
Chapter 1 Linear Invariant Subspaces in Quasilinear Equations: Basic Examples and Models -- chapter 2 Invariant Subspaces and Modules: Mathematics in One Dimension -- chapter 3 Parabolic Equations in One Dimension: Thin Film, Kuramoto-Sivashinsky, and Magma Models -- chapter 4 Odd-Order One-Dimensional Equations: Korteweg-de Vries, Compacton, Nonlinear Dispersion, and Harry Dym Models -- chapter 5 Quasilinear Wave and Boussinesq Models in One Dimension. Systems of Nonlinear Equations -- chapter 6 Applications to Nonlinear Partial Differential Equations in IR N -- chapter 7 Partially Invariant Subspaces, Invariant Sets, and Generalized Separation of Variables -- chapter 8 Sign-Invariants for Second-Order Parabolic Equations and Exact So- lutions -- chapter 9 Invariant Subspaces for Discrete Operators, Moving Mesh Methods, and Lattices.
Victor A. Galaktionov, Sergey R. Svirshchevskii.
Includes bibliographical references (pages 467-492) and index.
Boca Raton, FL : Chapman & Hall/CRC, ©2007
Chapman & Hall/CRC applied mathematics and nonlinear science series