I. Karpenko

collaborators

Showing math.APShow all

3 papers · 1 filter

math.AP2026

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 $u_{x t} = sin u$ in the quarter planes $x > 0$ , $t > 0$ …

math.AP2025

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 $m ~_{t} + ((u ~^{2} - u ~_{x}^{2} + 2 u ~) m ~)_{x} = 0$ , $\t…

math.AP2025

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…