Math 567: Some References
T. Tao, Nonlinear Dispersive Equations (2006)
-- a thorough introduction to the modern mathematical theory of
nonlinear waves. This is the text most closely aligned with this
course, especially Chs. 1-3, though in places it hits levels
of depth and sophistication that we will not.
G. Whitham, Linear and Nonlinear Waves (1974)
-- a classical 'applied' text. Part II covers many of the basic
notions for linear and nonlinear dipsersive PDE.
W. Strauss, Nonlinear Wave Equations (1989)
-- a short, efficient overview of the mathematical state-of-the-art
at the time.
C. Sulem, P.-L. Sulem, The Nonlinear Schroedinger Equation (1999)
G. Fibich, The Nonlinear Schroedinger Equation (2015)
-- these books cover many aspects of NLS, both analysis and applications
T. Cazenave, Semilinear Schroedinger Equations (2003)
-- full gory details of analysis of NLS
Analysis background: there are many standard texts, including
- G. Folland, Real Analysis: Modern Techniques and their
PDE background: again there are many standard texts, including
- W. Strauss, Partial Differential Equations
- L. Evans, Partial Differential Equations