Chapman and Hall/CRC
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 step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time.
Chapter 1: Inverse scattering problems for systems of rst-order ODEs on a half-line
Chapter 2: Some problems for a system of nonlinear evolution equations.on a half-line
Chapter 3: Some problems for cubic nonlinear evolution equations on a half-line
Chapter 4: The Dirichlet IBVPs for sine and sinh-Gordon equations
Chapter 5: Inverse scattering for integration of the continual system of nonlinear interaction waves
Chapter 6: Some problems for the KdV equation and associated inverse scattering
Chapter 7: Inverse scattering and its application to the KdV equation with dominant surface tension
Chapter 8: The inverse scattering problem for the perturbed string equation and its application to integration of the two-dimensional generalization from Korteweg-de Vries equation
Chapter 9: Connections between the inverse scattering method and related methods