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 Applications
  • PDE background: again there are many standard texts, including
    • W. Strauss, Partial Differential Equations (undergraduate level)
    • L. Evans, Partial Differential Equations (graudate level)