Nonlinear Equations with Small Parameter: Volume 2 Waves and Boundary Problems

• Publisher: De Gruyter
• Year: 2018
• Tongue: English
• Leaves: 442
• Series: De Gruyter Series in Nonlinear Analysis and Applications; 23/2
• Category: Library

✦ Synopsis

This is the second volume of Nonlinear Equations with Small Parameter containing new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. They allow one to match asymptotics of various properties with each other in transition regions and to get unified formulas for connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena. These are beginnings of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering constructions and quantum systems. Apart from independent interest the approximate solutions serve as a foolproof basis for testing numerical algorithms. The second volume will be related to partial differential equations.

• This second volume is related to asymptotics for partial differential equations.
• Covers autoresonances, solitons, and nonlinear Cauchy problems for elliptic operators.
• A fundamental study of asymptotics for nonlinear equations in two volumes.

✦ Table of Contents

Preface
Contents
Introduction
1. The Solitary Waves Generation due to Passage through the Local Resonance
2. Regular Perturbation of Ill-Posed Problems
3. Asymptotics at Characteristic Points
4. Asymptotic Expansions of Singular Perturbation Theory
5. Asymptotic Solution of the Schrödinger Equation
6. The Kelvin–Helmholtz Instability
7. Nonlinear Cauchy Problems for Elliptic Equations
Bibliography
Index