Abstract
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.
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