說明 
xxvi, 388 pages ; 25 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
系列 
Monographs and research notes in mathematics 

Monographs and research notes in mathematics

附註 
Includes bibliographical references and index 

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved stepbystep, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features " The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely." Solving the associated initial value problem or initialboundary value problem for the nonlinear evolution equations (NLEEs) is carried out stepbystep. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the timedependent scattering data (SD) are constructed from the initial and boundary conditions." The potentials are recovered uniquely in terms of timedependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP." Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM 
主題 
Inverse problems (Differential equations)


Nonlinear integral equations


Scattering (Mathematics)


Inverse problems (Differential equations) fast (OCoLC)fst00978098


Nonlinear integral equations. fast (OCoLC)fst01038791

