Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation

Details Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation

2009-08-15

arxiv.org/abs/0908.2152v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 4 figures

Scientific paper

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 behaviour 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 $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.

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