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By Roger Grimshaw

The paintings covers asymptotic equipment for the derivation of canonical evolution equations, corresponding to the Korteweg-deVries and nonlinear Schrödinger equations, descriptions of the elemental resolution units of those evolution equations, and the main proper and compelling functions. those topics are interlocked, and it will be tested during the textual content. the subjects handle any fluid move program, yet there's a bias in the direction of geophysical fluid dynamics, reflecting for the main half the components the place many purposes been stumbled on.

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Extra resources for Nonlinear Waves in Fluids: Recent Advances and Modern Applications

Example text

It is due to the seminal work of Benjamin and Feir (1967) which combined experimental evidence with a weakly nonlinear theory. Mathematically, the BF instability can be characterized as a collision of two pairs of purely imaginary eigenvalues of opposite energy sign (see Figure 3 for a schematic). For the full water-wave problem, there is in addition to the four eigenvalues shown in Figure 3 a countable number of stable purely imaginary eigenvalues. This point of view of the BF instability was a byproduct of the proof of the BF instability provided by Bridges and Mielke (1995).

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V. L Nekorkin and M. G. Velarde. Synergetic Phenomena in Active Lattices. Patterns, Waves, Solitons, Chaos. Springer-Verlag, Berlin, 2002. C. Newell. Solitons in mathematics and physics. CBMS-NSF Series in Applied Mathematics 48, SIAM, Phfladelphia, 1985. A. Ostrovsky. Nonlinear internal waves in rotating fiuids. oceanology, 18: 181-191, 1978. L. J. Weinstein. Convective linear stability of solitary waves for Boussinesq equations. , 99: 311-375, 1997. Lord Rayleigh. On waves. Phil. Mag. 1: 257-279, 1876.

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