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Math 567: Some References
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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.
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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.
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W. Strauss, Nonlinear Wave Equations (1989)
-- a short, efficient overview of the mathematical state-of-the-art
at the time.
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C. Sulem, P.-L. Sulem, The Nonlinear Schroedinger Equation (1999)
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G. Fibich, The Nonlinear Schroedinger Equation (2015)
-- these books cover many aspects of NLS, both analysis and applications
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T. Cazenave, Semilinear Schroedinger Equations (2003)
-- full gory details of analysis of NLS
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Analysis background: there are many standard texts, including
- G. Folland, Real Analysis: Modern Techniques and their
Applications
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PDE background: again there are many standard texts, including
- W. Strauss, Partial Differential Equations
(undergraduate level)
- L. Evans, Partial Differential Equations
(graudate level)
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