5 citations · 5 across the 1 of their papers we have counts for
3 papers
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…
A Riemann-Hilbert approach to the modified Camassa-Holm equation with nonzero boundary conditions
Anne Boutet de Monvel, Iryna Karpenko, Dmitry Shepelsky
The paper aims at developing the Riemann-Hilbert problem approach to the modified Camassa-Holm (mCH) equation in the case when the solution is assumed to approach a non-zero consta…
Nonlinear Fourier spectrum characterization of time-limited signals
Dmitry Shepelsky, Anastasiia Vasylchenkova, Jaroslaw E. Prilepsky +1
Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide an explicit proof for the properties o…