4 papers
The direct scattering problem for the defocusing nonlinear Schrödinger equation with step-like periodic background
Dinghao Zhu
We consider the defocusing nonlinear Schrödinger equation for step-like data connecting two, in general different, genus-one periodic states. Starting from the Jost solutions assoc…
Arbitrary-genus dark soliton gases in the defocusing nonlinear Schrödinger hydrodynamics
Marco Bertola, Deng-Shan Wang, Peng Yan +1
The defocusing nonlinear Schrödinger hydrodynamics supports exact dark solitons under finite density boundary conditions. However, the dark soliton gas, an interacting ensemble of…
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…
Focusing and defocusing mKdV equation with fully asymmetric nonzero boundary conditions: the inverse scattering transform
Zhao Yi, Zhu Dinghao
In this paper, we investigate the inverse scattering transform(IST) for the focusing and defocusing mKdV equation with fully asymmetric nonzero boundary conditions. Our analysis fo…