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Asymptotic soliton train solutions of Kaup–Boussinesq equations

✍ Scribed by A.M Kamchatnov; R.A Kraenkel; B.A Umarov

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
162 KB
Volume
38
Category
Article
ISSN
0165-2125

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✦ Synopsis

Asymptotic soliton trains arising from a 'large and smooth' enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup-Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr-Sommerfeld quantization rule which generalizes the usual rule to the case of 'two potentials' h 0 (x) and u 0 (x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u 0 (x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup-Boussinesq equations with predictions of the asymptotic theory is found.

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