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Sinopsis
Preface to the Third Edition.- Preface.- Linear Partial Differential Equations.- Nonlinear Model Equations and Variational Principles.- First-Order, Quasi-Linear Equations and Method of Characteristics.- First-Order Nonlinear Equations and Their Applications.- Conservation Laws and Shock Waves.- Kinematic Waves and Real-World Nonlinear Problems.- Nonlinear Dispersive Waves and Whitham’s Equations.- Nonlinear Diffusion-Reaction Phenomena.- Solitons and the Inverse Scattering Transform.- The Nonlinear Schroedinger Equation and Solitary Waves.- Nonlinear Klein--Gordon and Sine-Gordon Equations.- Asymptotic Methods and Nonlinear Evolution Equations.- Tables of Integral Transforms.- Answers and Hints to Selected Exercises.- Bibliography.- Index.
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Acerca del autor
Lokenath Debnath is author or co-author of seven graduate-level books and research monographs, including "Introduction to Hilbert Spaces with Applications," "Nonlinear Water Waves," and "Continuum Mechanics" published by Academic Press; "Nonlinear Partial Differential Equations for Scientists and Engineers" and "Wavelets Transforms and Their Applications," published by Birkhauser Boston; "Partial Differential Equations for Scientists and Engineers" published by Prentice Hall; and "Integral Transforms and Their Applications" by CRC Press/Chapman and Hall. He has also edited seven research monographs including "Nonlinear Waves" published by Cambridge University Press and "Wavelet Transforms and Time-Frequency Signal Analysis" published by Birkhauser Boston. He is an author and co-author of over 300 research papers in pure and applied mathematics, encompassing applied partial differential equations, integral transforms and special functions, inequalities, solid and fluid mechanics, linear and nonlinear waves, solitons, magnetohydrodynamics, unsteady boundary layers, dynamics of oceans, wavelet transforms, signal processing, and stability theory.
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<p><i>An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here.</i> <b>—Applied Mechanics Review (Review of First Edition)</b></p><p><i>Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library.</i> <b>—UK Nonlinear News (Review of Second Edition)</b></p><p>The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their various current applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications have been chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. </p><p>The book gives thorough coverage of the derivation and solution methods for all fundamental nonlinear model equations, such as Korteweg–de Vries, Camassa–Holm, Degasperis–Procesi, Euler–Poincaré, Toda lattice, Boussinesq, Burgers, Fisher, Whitham, nonlinear Klein–Gordon, sine-Gordon, nonlinear Schrödinger, nonlinear reaction-diffusion, and Euler–Lagrange equations. Other topics and key features include: </p><p>* Improved presentations of results, solution methods, and proofs. </p><p>* Solitons, gravity-capillary solitary waves, and the Inverse Scattering Transform. </p><p>* Special emphasis on compactons, intrinsic localized modes, and nonlinear instability of dispersive waves with applications to water waves and wave breaking phenomena. </p><p>* New section on the Lorenz nonlinear system, the Lorenz attractor, and deterministic chaos, and new examples of nonlinear quasi-harmonic waves, modulational instability, nonlinear lattices, and the Toda lattice equation. </p><p>* Over 1000 worked-out examples and end-of-chapter exercises with expanded hints and answers to selected exercises. </p><p>* Two new appendices on some special functions and their basic properties, Fourier series, generalized functions, and Fourier and Laplace transforms, with algebraic and analytical properties of convolutions and applications. </p><p>* Many aspects of modern theory that will put the reader at the forefront of current research.</p><p>* Completely updated list of references and enlarged index. </p><p><i>Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition</i>, improves on an already complete and accessible resource for senior undergraduate and graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, a research reference, or a self-study guide.</p><p></p>
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