Solitons, Nonlinear Evolution Equations and Inverse Scattering

Author: Mark J. Ablowitz

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 516

View: 281

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

Author: M. A. Ablowitz

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 532

View: 225

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Direct and Inverse Methods in Nonlinear Evolution Equations

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999

Author: Robert M. Conte

Publisher: Springer Science & Business Media

ISBN:

Category: Science

Page: 279

View: 324

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.

Nonlinear Dynamics

Integrability, Chaos and Patterns

Author: Muthusamy Lakshmanan

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 620

View: 502

This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Topics in Soliton Theory and Exactly Solvable Nonlinear Equations

Proceedings of the Conference on Nonlinear Evolution Equations, Solitons and the Inverse Scattering Transform, Oberwolfach, Germany, July 27-August 2, 1986

Author: Benno Fuchssteiner

Publisher: World Scientific Publishing Company Incorporated

ISBN:

Category: Differential equations, Nonlinear

Page: 342

View: 297

Integrable Hamiltonian Hierarchies

Spectral and Geometric Methods

Author: Vladimir Gerdjikov

Publisher: Springer Science & Business Media

ISBN:

Category: Science

Page: 643

View: 389

This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Introduction to Nonlinear Dispersive Equations

Author: Felipe Linares

Publisher: Springer

ISBN:

Category: Mathematics

Page: 301

View: 240

This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.

Nonlinear Wave Equations

Author: Satyanad Kichenassamy

Publisher: CRC Press

ISBN:

Category: Science

Page: 296

View: 609

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Nonlinear Waves in Integrable and Nonintegrable Systems

Author: Jianke Yang

Publisher: SIAM

ISBN:

Category: Nonlinear waves

Page: 430

View: 512

Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.