Nonlinear Theory of Pseudodifferential Equations on a Half-line

This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal.

· For the first time the definition of pseudodifferential operator on a half-line and a segment is done
· A wide class of nonlinear nonlocal and local equations is considered
· Developed theory is general and applicable to different equations
· The book is written clearly, many examples are considered
· Asymptotic formulas can be used for numerical computations by engineers and physicists
· The authors are recognized experts in the nonlinear wave phenomena

Introduction
1 Preliminaries
2 Sobolev spaces
3 General Theory
4 Nonlinear Schrodinger Type Equations
5 Whitham Equation
6 Korteweg-de Vries-Burgers Equation
7 Large Initial Data
8 KdV-B Type Equation
9 Dirichlet Problem for KdV Equation
10 Neumann Problem for KdV Equation
11 Landau-Ginzburg Equations
12 Burgers Equation with Pumping
13 KdVB Equation on a Segment
14 NLS Equation on Segment
15 Periodic Problem
Bibliography
Index