Abstract
These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed discussions are avoided. Many of the topics require only a standard background in applied mathematics.
The lectures deal with the following topics: fundamentals of linear and nonlinear wave motion; isospectral flows with associated compatible linear systems including PDE’s in 1+1 and 2+1 dimensions, with remarks on differential-difference and partial difference equations; the Inverse Scattering Transform (IST) for decaying initial data on the infinite line for problems in 1+1 dimensions; IST for 2+1 dimensional problems; remarks on self-dual Yang-Mills equations and their reductions. The first topic is extremely broad, but a brief review provides motivation for the other subjects covered in these lectures.
Keywords
- Solitary Wave
- Nonlinear Wave
- Nonlinear Evolution Equation
- Gauge Algebra
- London Mathematical Society Lecture Note
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Ablowitz, M. Nonlinear Waves, Solitons, and IST. In: Kosmann-Schwarzbach, Y., Tamizhmani, K.M., Grammaticos, B. (eds) Integrability of Nonlinear Systems. Lecture Notes in Physics, vol 638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40962-5_2
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DOI: https://doi.org/10.1007/978-3-540-40962-5_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20630-9
Online ISBN: 978-3-540-40962-5
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