Nonlinear Partial Differential Equations for Scientists and Engineers

1. Front Matter

   Pages I-XXIII

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2. Linear Partial Differential Equations

   • Lokenath Debnath

   Pages 1-147

3. Nonlinear Model Equations and Variational Principles

   • Lokenath Debnath

   Pages 149-199

4. First-Order, Quasi-linear Equations and Method of Characteristics

   • Lokenath Debnath

   Pages 201-226

5. First-Order Nonlinear Equations and Their Applications

   • Lokenath Debnath

   Pages 227-256

6. Conservation Laws and Shock Waves

   • Lokenath Debnath

   Pages 257-281

7. Kinematic Waves and Real-World Nonlinear Problems

   • Lokenath Debnath

   Pages 283-354

8. Nonlinear Dispersive Waves and Whitham’s Equations

   • Lokenath Debnath

   Pages 355-379

9. Nonlinear Diffusion–Reaction Phenomena

   • Lokenath Debnath

   Pages 381-423

10. Solitons and the Inverse Scattering Transform

    • Lokenath Debnath

    Pages 425-533

11. The Nonlinear Schrödinger Equation and Solitary Waves

    • Lokenath Debnath

    Pages 535-577

12. Nonlinear Klein–Gordon and Sine-Gordon Equations

    • Lokenath Debnath

    Pages 579-622

13. Asymptotic Methods and Nonlinear Evolution Equations

    • Lokenath Debnath

    Pages 623-674

14. Tables of Integral Transforms

    • Lokenath Debnath

    Pages 675-687

15. Back Matter

    Pages 689-860

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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 varied and updated applications.  In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation.

Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.

• applied mathematics
• computational methods
• engineering
• mathematical physics
• partial differential equations

From the reviews:

"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)

From the reviews of the third 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)

“This book provides an introduction to nonlinear partial differential equations that arise throughout in science and engineering and to the basic methods for finding the solutions for these equations. The book contains thirteen chapters and three appendixes. At the end of the first twelve chapters there are exercises that help to understand the subject matter. … This book is recommended for graduate students in science and engineering.” (Valery V. Karachik, Zentralblatt MATH, Vol. 1242, 2012)

• , Department of Mathematics, University of Texas, Pan American, Edinburg, USA

  Lokenath Debnath

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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