4 papers
Direct Scattering for the KdV Equation with a Step-like Finite-Gap Potential: A Riemann--Hilbert Approach
Xiaodong Zhu
We develop the direct scattering theory for the KdV equation with step-like finite-gap backgrounds under perturbations. More precisely, we consider initial data that asymptotically…
Long-time asymptotics of the good Boussinesq equation and its modified version: Painlevé region
Deng-Shan Wang, Xiaodong Zhu
This work investigates the long-time asymptotic behaviors of initial value problem for the good Boussinesq equation and the modified Boussinesq equation in Painlevé region. The Dei…
Long-time asymptotics of the Sawada-Kotera equation on the line
Deng-Shan Wang, Xiaodong Zhu
The Sawada-Kotera (SK) equation is an integrable system characterized by a third-order Lax operator and is related to the modified Sawada-Kotera (mSK) equation through a Miura tran…
Genus two KdV soliton gases and their long-time asymptotics
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu
This paper employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus Korteweg-de Vries soliton gases. It is demonstrated…