227 citations · 381 across the 24 of their papers we have counts for
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The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem
Anne Boutet de Monvel, Iryna Karpenko, Dmitry Shepelsky
This paper deals with the Cauchy problem for the modified Camassa-Holm (mCH) equation \begin{alignat*}{4} &m_t+\left((u^2-u_x^2)m\right)_x=0,&\quad&m:= u-u_{xx},&\quad&t>0,&\;&-\in…
The focusing NLS equation with step-like oscillating background: asymptotics in a transition zone
Anne Boutet de Monvel, Jonatan Lenells, Dmitry Shepelsky
In a recent paper, we presented scenarios of long-time asymptotics for a solution of the focusing nonlinear Schrödinger equation whose initial data approach two different plane wav…
The focusing NLS equation with step-like oscillating background: the genus 3 sector
Anne Boutet de Monvel, Jonatan Lenells, Dmitry Shepelsky
We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching different plane waves $A_j\mathrm{e}^{\mathrm{i}ϕ_j}\mathrm{e}^{-2\math…
The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics
Anne Boutet de Monvel, Jonatan Lenells, Dmitry Shepelsky
We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching two different plane waves $A_j\mathrm{e}^{\mathrm{i}ϕ_j}\mathrm{e}^{-2\…