integrable systems 1nonlocal mKdV equation 1riemann-hilbert problem 1soliton solutions 1step-like initial data 1
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math.AP2026
Riemann-Hilbert approach for the nonlocal modified Korteweg-de Vries equation with a step-like oscillating background
Yan Rybalko
The paper develops a Riemann‑Hilbert framework for solving the Cauchy problem of the nonlocal modified Korteweg‑de Vries equation with oscillating step‑like boundary conditions and…
math.AP2025
The integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: long-time asymptotics
Yan Rybalko, Dmitry Shepelsky, Shou-Fu Tian
We consider the Cauchy problem for the integrable nonlocal nonlinear Schrödinger equation \[ \I q_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0, \] subject to the step-like ini…