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.

PACS numbers: 05.40−a, 05.45.Yv, 47.54.−r

Print publication: Issue 47 (27 November 2009)
Received 13 August 2009, in final form 7 October 2009
Published 4 November 2009