4 citations · 4 across the 6 of their papers we have counts for
7 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
Under suitable solitonless assumptions on the associated scattering data, we rigorously establish the long-time asymptotics of the modified Boussinesq equation in the Painlevé regi…
Riemann-Hilbert problem and long-time asymptotics of the Yajima-Oikawa equation
Deng-Shan Wang, Yingmin Yang, Xiaodong Zhu
The Yajima-Oikawa equation is an integrable long wave-short wave resonance interaction model arising as a deformation of the Zakharov system for Langmuir waves coupled to ion-acous…
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…
Long-time asymptotics of the Tzitzéica equation on the line
Lin Huang, Deng-Shan Wang, Xiaodong Zhu
In this paper, the renowned Riemann-Hilbert method is employed to investigate the initial value problem of Tzitzéica equation on the line. Initially, our analysis focuses on elucid…
Miura transformations and large-time behaviors of the Hirota-Satsuma equation
Deng-Shan Wang, Cheng Zhu, Xiaodong Zhu
The good Boussinesq equation has several modified versions such as the modified Boussinesq equation, Mikhailov-Lenells equation and Hirota-Satsuma equation. This work builds the fu…