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Evolution equations, Nonlinear.

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This book shows that the physical phenomena and processes that take place in nature generally have complicated nonlinear features, which leads to nonlinear mathematical models for the real processes. It focuses on the practical issues involved here, as well as the development of methods to investigate the associated nonlinear mathematical problems, including nonlinear wave propagation. It acquaints the reader with a series of methods and approaches that can be applied to a wide class of nonlinear equations. The book also outlines a way in which an uninitiated reader could investigate a new nonlinear equation.

Evolution equations, Nonlinear.

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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.

Evolution equations, Nonlinear. --- Pseudodifferential operators.

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Evolution equations, Nonlinear --- Differential equations, Partial

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Solitons --- Nonlinear optics --- Evolution equations, Nonlinear