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.
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.
"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."--Applied Mechanics Review (Review of First Edition) "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."--UK Nonlinear News (Review of Second Edition)