Some aspects of non-linear dispersive waves in a randomly inhomogeneous medium are considered. The wave motion is governed by the Korteweg-de Vries (KdV) equation with randomly varying coefficients. The effect of a random inhomogeneity on the KdV invariants and on the soliton disintegration (splitting) is discussed. Also, the evolution of the mean (or, coherent) solitary waves is analyzed; the deformation (damping) of the KdV soliton due to the randomness of the medium is shown explicitly. © 1991.
Sobczyk, K. (1992). Korteweg-de vries solitons in a randomly varying medium. International Journal of Non-Linear Mechanics, 27(1), 1–8. https://doi.org/10.1016/0020-7462(92)90018-3