29 citations · 39 across the 6 of their papers we have counts for
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The Short Wave equation on the half-line by the Unified Transform Method
Iryna Karpenko, Dmitry Shepelsky, Ilona Tylevna
We study the initial-boundary value problem for the Short Wave equation on the half-line . A distinctive feature of this problem is that the boundary cannot be charac…
The sine Gordon equation in light-cone coordinates on the half lines revisited: a Riemann--Hilbert approach
Iryna Karpenko
In this work, we study the initial boundary value (IBV) problems for the sine-Gordon (sG) equation in the light-cone coordinates in the quarter planes , …
The modified Camassa-Holm equation on the half line: a Riemann--Hilbert approach
Iryna Karpenko, Dmitry Shepelsky
We consider the initial-boundary value (IBV) problem for the modified Camassa--Holm (mCH) equation , $\t…
The periodic Camassa-Holm equation by the Riemann-Hilbert problem approach
Anne Boutet de Monvel, Iryna Karpenko, Dmitry Shepelsky +1
This work addresses the development of the Riemann-Hilbert problem (RHP) formalism (the Fokas method) for the Camassa-Holm equation under periodic boundary conditions. Particularly…
A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions
Iryna Karpenko, Dmitry Shepelsky, Gerald Teschl
The paper aims at developing the Riemann-Hilbert (RH) approach for the modified Camassa-Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solu…
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…