Yeojin Chung 2009 J. Phys. A: Math. Theor. 42 475002 doi:10.1088/1751-8113/42/47/475002
Yeojin Chung
Show affiliationsWe 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.
02.30.Jr Partial differential equations
02.60.Cb Numerical simulation; solution of equations
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
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
Issue 47 (27 November 2009)
Received 13 August 2009, in final form 7 October 2009
Published 4 November 2009
Yeojin Chung 2009 J. Phys. A: Math. Theor. 42 475002
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