Korteweg-de Vries and Nonlinear Schrödinger Equations
Subtitle: Qualitative Theory (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: May 18, 2001
Language: eng
Format: Paperback
Number of pages: 147
ISBN-13: 9783540418337
Subjects: Differential Equations; Integral Equations; Partial Differential Equations; Mathematics; Science/Mathematics; Differential Equations - Partial Differential Equations; General; Mathematical Physics; Mathematics / Differential Equations; Well-posedness; invariant measure; stability; stationary solution; Mathematical Analysis; Korteweg-de Vries equation; Schrodinger equation; Schrèodinger equation
Description: The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.