Laguerre polynomials and transitional asymptotics of the modified Korteweg-de Vries equation for step-like initial data

Marco Bertola, Alexander Minakov

We consider the compressive wave for the modified Korteweg--de Vries equation with background constants $c>0$ for $x\to -\infty$ and $0$ for $x\to +\infty .$ We study the asymptotics…