"Nonlinear partial differential equations is an old and vast area of research. There is a big and well-developed theory as well as a huge variety of applications. It seems to be impossible to embrace this subject in a single monograph. The book of Lokenath Debnath is a quite successful attempt. It is a second edition of the book, considerably extended and revised. The author is trying to balance the deep and rigorous theory and a variety of approaches and often seminal examples. To examples, he gives the leading, more than just an illustrative, role. The book could serve as a good selection of choices for a kernel of a graduate or even undergraduate module in Applied Mathematics or Engineering Sciences.

For more fundamental courses the book is also useful, since it contains a lot of motivations and well elaborated exercises. 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." a?UK Nonlinear News (Review of Second Edition)   "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. The style is clear and to the point. This is a very useful book for all scientists dealing with nonlinear phenomena. This reviewer feels that it is a very hard act to follow, and recommends it strongly for individual students, practitioners, and libraries alike.

The reviewer seldom gets so enthusiastic about the books he is asked to review, but [this book] is a jewel." a?Applied Mechanics Review (Review of First Edition)   "This book provides a valuable survey ofa? nonlinear partial differential equations and their methods of solutionsa? at the end of each chapter [there are] exercises that help build an understanding of the subject matter, a? and in many cases [these exercises] provide an extension of material found in the main body of the texta? the style of writing is clear and concise and the choice of topics is comprehensive." a?Zentralblatt Math (Review of First Edition) "The book is written in a lucid, no-nonsense style that will be a pleasure for any serious reader. The author's emphasis is on the physical significance of the solutions and less on such mathematical subtleties as existence and uniqueness properties.The text is designed and organized primarily for classroom use. It can be used selectively, or the whole book can be used for a two-semester course. It can also serve as a reference and as a starting point for further study. Each chapter contains numerous, well-chosen exercises, and selected solutions are provided at the end of the book, making it suitable for self-study.

I hope this book will succeed in bringing new developments in PDEs to those classrooms in which students have so far been limited to the classical results." a?Computing Reviews (Review of First Edition) "In an effort to make the book useful for a diverse readership, 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." a?Booknews (Review of First Edition).