Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations

Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations,Second Edition is a book that discusses inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). It is suitable for anyone with a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. The problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students. The book also discusses the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line.

Format: Hardback
Length: 422 pages
Publication date: 15 May 2023
Publisher: Taylor & Francis Ltd

Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations,Second Edition is a comprehensive guide to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). This book is designed for individuals with a mathematical background and a keen interest in functional analysis, differential equations, and equations of mathematical physics. The book serves as a valuable resource for a wide community engaged in ISPs and their applications, with a particularly strong traditional community in mathematical physics.

The monograph presents the problems step-by-step, providing detailed proofs to enhance accessibility for students encountering these topics for the first time. Notable additions to the Second Edition include a new chapter on the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line. Updated references and concluding remarks further enrich the content.

The book focuses on solving the direct and ISP, followed by solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs. The unknown boundary values are calculated using the Lax (generalized) equations, and the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. This allows for the unique recovery of potential functions in terms of the given initial and calculated boundary conditions. The solvability of the ISP is established, and the SD of the scattering problem is fully described. Numerous ISPs are thoroughly solved, showcasing the effectiveness of the proposed methods.

The ISPs are set up in a way that facilitates the construction of Bӓckhund transformations (BTs) for so. By employing these transformations, the solutions of NLEEs can be transformed into solutions of the corresponding linear equations in the Lax pair. This opens up new avenues for studying and understanding the behavior of NLEEs.

In summary, Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations,Second Edition is a indispensable resource for researchers, scholars, and students in mathematics, physics, and related fields. It provides a comprehensive treatment of ISPs and their applications, offering detailed explanations, proofs, and practical examples. With its updated content and broad appeal, this book is destined to become a staple in the study of inverse scattering and its applications to nonlinear evolution equations.

Weight: 1000g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032429212
Edition number: 2 ed