1304.1703 (Minakov Alexander)

Modified Korteweg-de Vries equation: modulated elliptic wave and a train
of asymptotic solitons    [PDF]

Minakov Alexander

This paper is devoted to the long-time asymptotic analysis of the Cauchy problem for the modified Korteweg -- de Vries equation with a step-like initial function, which rapidly tends to different constants as $x\to\pm\infty$. First investigations of this problem were done by E. Khruslov and V. Kotlyarov in 1989. By using the technique, developed by E. Khruslov for the Korteweg -- de Vries equation in 1976, they studied the long-time asymptotic behavior of this problem solution in the domain $x>4c^2t-const \log t$, and found (discovered) that the solution breaks (splits) up into a train of so-called asymptotic solitons in the subdomain $4c^2t-const \log tView original: http://arxiv.org/abs/1304.1703