Nearly linear dynamics of nonlinear dispersive waves

Details Nearly linear dynamics of nonlinear dispersive waves Nearly linear dynamics of nonlinear dispersive waves

2010-09-29

arxiv.org/abs/1009.5930v1

Physics

Mathematical Physics

21 pages, 6 figures

Scientific paper

Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.

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