Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations (Chapman & Hall/Crc Monographs and Research Notes in Mathematics) - Hardcover

Vu, Pham Loi

Hardcover

ISBN 10: 1032429216 ISBN 13: 9781032429212

Verlag: Chapman and Hall/CRC, 2023

Inhaltsangabe

Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics.

In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time.

New to the Second Edition

All new chapter dealing with 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

Features

• Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved.
• The ISPs are set up appropriately for constructing the B?ckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space.
• The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.

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Über die Autorin bzw. den Autor

Pham Loi Vu, PhD is a professor, and a leading Vietnamese expert in inverse problems and their applications. He has authored 50 papers published in prominent journals, including Inverse Problems (Q1), Acta Applicandae Mathematicae (Q2), Journal of Nonlinear Mathematical Physics (Q2), and others.

His previous research focused on seismic waves in seismic prospecting for petroleum-gas complexes and on determining coordinates of epicenter in near earthquakes at the Institute of Geophysics of the Vietnam Academy. He is now a researcher at VAST's Institute of Mechanics and the National Foundation for Science and Technology Development (NAFOSTED).

Von der hinteren Coverseite

This book is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics.

Details zur Ausgabe

• Verlag: Chapman and Hall/CRC
• Erscheinungsdatum: 2023
• Sprache: Englisch
• ISBN 10: 1032429216
• ISBN 13: 9781032429212
• Einband: Gebundene Ausgabe
• Auflage: 2
• Anzahl der Seiten: 456
• Kontakt zum Hersteller: preigu GmbH & Co. KG; mail@preigu.de; ; Lengericher Landstr. 19; Osnabrück; Niedersachsen; 49078; Deutschland