Soliton dynamics in a random Toda chain.

This paper addresses the soliton dynamics in a Toda lattice with a randomly distributed chain of masses. Applying the inverse scattering transform, we derive effective equations for the decay of the soliton amplitude that take into account radiative losses. It is shown that the soliton energy decays as approximately N(-3/2) for small-amplitude solitons and approximately exp(-N) for large-amplitude solitons. The decay rate does not depend on the incoming energy for large-amplitude soliton. An important feature is the generation of a soliton gas consisting of a large collection of small solitons (a number of the order of epsilon (-2) of solitons with momenta of the order of epsilon (2), where epsilon is the strength of fluctuations). The soliton gas plays an important role in that the changes in the conservation equations cannot be correctly understood if the soliton production is neglected. The role of the correlation length of fluctuations on the soliton decay is discussed. It is shown that in the presence of long-range correlation the Toda soliton is not backscattered, but progressively converted into forward-going radiation. The analytical predictions are confirmed by full numerical simulations.

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