**Translations of Mathematical Monographs**

1994;
289 pp;
Hardcover

MSC: Primary 35; 45;
Secondary 76

**Print ISBN: 978-0-8218-4573-8
Product Code: MMONO/133**

List Price: $128.00

AMS Member Price: $102.40

MAA Member Price: $115.20

**Electronic ISBN: 978-1-4704-4541-6
Product Code: MMONO/133.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

# Nonlinear Nonlocal Equations in the Theory of Waves

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*P. I. Naumkin; I. A. Shishmarev*

This book is the first to concentrate on the theory of nonlinear nonlocal equations. The authors solve a number of problems concerning the asymptotic behavior of solutions of nonlinear evolution equations, the blow-up of solutions, and the global in time existence of solutions. In addition, a new classification of nonlinear nonlocal equations is introduced. A large class of these equations is treated by a single method, the main features of which are apriori estimates in different integral norms and use of the Fourier transform. This book will interest specialists in partial differential equations, as well as physicists and engineers.

#### Readership

Specialists in partial differential equations.

#### Reviews & Endorsements

The book is a good exposition of important results. Many examples are considered. The style of the book is systematic and readable.

-- Zentralblatt MATH

ExcellenDt contribution to the study of wave propagation…

-- Mathematical Reviews

Very readable … will be a source of inspiration not only to those who study nonlinear wave equations, but to all who like to see hard problems solved by masterful use of basic techniques.

-- Bulletin of the AMS

#### Table of Contents

# Table of Contents

## Nonlinear Nonlocal Equations in the Theory of Waves

- Cover Cover11
- Title page v6
- Contents vii8
- Introduction 112
- Chapter 1. Simplest properties of solutions of nonlinear nonlocal equations 1122
- Chapter 2. The Cauchy problem for the Whitham equation 2940
- Chapter 3. The periodic problem 6576
- Chapter 4. The system of equations of surface waves 89100
- Chapter 5. Generalized solutions 141152
- Chapter 6. The asymptotics as 𝑡>(∞) of solutions of the generalized Kolmogorov-Petrovskii-Piskunov equation 159170
- Chapter 7. Asymptotics of solutions of the Whitham equation for large times 179190
- Chapter 8. Asymptotics as 𝑡>(∞) of solutions of the nonlinear nonlocal Schrodinger equation 209220
- Chapter 9. Asymptotics of solutions for a system of equations of surface waves for large times 235246
- Chapter 10. The step-decaying problem for the Korteweg-de Vries-Burgers equation 261272
- Bibliography 281292
- Back Cover Back Cover1305