Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations, 2nd Edition eBook

Delivery: Can be download immediately after purchasing. For new customer, we need process for verification from 30 mins to 12 hours.
Version: PDF/EPUB. If you need EPUB and MOBI Version, please contact us.
Compatible Devices: Can be read on any devices.

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 Bӓckhund 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.

This is a digital product.

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations 2nd Edition is written by Pham Loi Vu and published by Chapman & Hall. The Digital and eTextbook ISBNs for Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations are 9781000872125, 1000872122 and the print ISBNs are 9781032429212, 1032429216. Additional ISBNs for this eTextbook include 9781003370543, 9781032441160, 9781000872057.