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A numerical study of the diverging probability density function of flat-top solitons in an extended Korteweg–de Vries equation

Yeojin Chung

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We consider an extended Korteweg–de Vries (eKdV) equation, the usual Korteweg–de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behavior of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter κ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible κ value.


PACS

05.45.Yv Solitons

02.30.Jr Partial differential equations

47.35.Fg Solitary waves

02.60.Cb Numerical simulation; solution of equations

02.50.Cw Probability theory

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

MSC

82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)

60Bxx Probability theory on algebraic and topological structures

60G50 Sums of independent random variables; random walks

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

35Q51 Solitons (See also 37K40)

76B25 Solitary waves (See also 35Q51)

Subjects

Fluid dynamics

Mathematical physics

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 47 (27 November 2009)

Received 13 August 2009, in final form 7 October 2009

Published 4 November 2009



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