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Singular Limits of Dispersive Waves (Paperback, Softcover reprint of the original 1st ed. 1994)
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Singular Limits of Dispersive Waves (Paperback, Softcover reprint of the original 1st ed. 1994)
Series: NATO Science Series B:, 320
Expected to ship within 10 - 15 working days
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The subject, of "Singular Limits of Dispersive vVaves" had its
modern origins in the 1960's when Whitham introduced the first
systematic approach to the asymptotic analysis of nonlinear
wavepackds. Initially developed through a variational principle
applied to the modulation of families of traveling wave solutions,
he soon realized that an efficient derivation of modulation
eq'uations could b(' accomplished by av- eraging local conservation
laws. He carried out this analysis for a wide variety of dispersive
nonlinear wave equations including the nonlinear Klein Gordon, KdV,
and NLS equations. The seminal work of Gardner, Greene, Kruskal and
Miura led to the discovery of partial differential equations which
are completely integrable through inverse spectral transforms. This
provided a larger framework in which to develop modulation theory.
In particular, one could consider the local modulation of families
of quasiperiodic so- lutions with an arbitrary number ofphases.
extending the sillglf' phase traveling waves treated Ly \Vhitham.
The first to extend vVhitham's ideas to the mllltiphase setting
were Flaschka, Forest and lvIcLaughlin, who derived N-phase
modulation equations for the KdV equation. By using geometric
techniques from the theory of Riemann surfaces they presented these
equations in Riemann invariant form and demonstrated their
hyperbolicity.
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