This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current...

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields.

One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behaviour of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades in the 20th century, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time...