A. Minakov

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math-ph2019

On the long time asymptotic behavior of the modified Korteweg de Vries equation with step-like initial data

Tamara Grava, Alexader Minakov

We study the long time asymptotic behaviour of the solution $q (x, t)$ , to the modified Korteweg de Vries equation (MKDV) $q_{t} + 6 q^{2} q_{x} + q_{xxx} = 0$ with step-like initial datum q(x,t=…

math-ph2019

Dispersive Shock Wave, Generalized Laguerre Polynomials and Asymptotic Solitons of the Focusing Nonlinear Schrödinger Equation

Vladimir Kotlyarov, Alexander Minakov

We consider dispersive shock wave to the focusing nonlinear Schrödinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi…

math-ph2017

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…