227 citations · 381 across the 24 of their papers we have counts for
25 papers
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…
Limiting distributions of ergodic continuous-time quantum walks on periodic graphs
Anne Boutet de Monvel, Kiran Kumar A. S., Mostafa Sabri
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For th…
Ergodic theorems for continuous-time quantum walks on crystal lattices and the torus
Anne Boutet de Monvel, Mostafa Sabri
We give several quantum dynamical analogs of the classical Kronecker-Weyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to…
Focusing nonlocal nonlinear Schrödinger equation with asymmetric boundary conditions: large-time behavior
Anne Boutet de Monvel, Yan Rybalko, Dmitry Shepelsky
We consider the focusing integrable nonlocal nonlinear Schrödinger equation \[\mathrm{i}q_{t}(x,t)+q_{xx}(x,t)+2q^{2}(x,t)\bar{q}(-x,t)=0\] with asymmetric nonzero boundary conditi…
Ballistic transport in periodic and random media
Anne Boutet de Monvel, Mostafa Sabri
We prove ballistic transport of all orders, that is, , for the following models: the adjacency matrix on , the…
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…