9 papers
On the global well-posedness for the nonlocal Fokas-Lenells equation with the weighted Sobolev initial data on the line
Zhenya Yan, Guoqiang Zhang, Guancheng Zhu
We establish the global well-posedness of the Cauchy problem for the reverse space-time nonlocal Fokas-Lenells equation with the weighted Sobolev initial data $q_0(x)\in H^{3}(\mat…
Long-time asymptotic behavior for the defocusing Hirota equation on a finite-genus algebro-geometric background
Taohua Luo, Zhenya Yan, Guoqiang Zhang
In this paper, we investigate the long-time asymptotics for the solution of the Cauchy problem of the defocusing Hirota equation on a finite-genus algebro-geometric background in t…
Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schrödinger equation
Ming Zhong, Weifang Weng, Zhenya Yan
We investigate the asymmetric integrable turbulence and rogue waves (RWs) emerging from the modulation instability (MI) of plane waves for the DNLS equation. The \(n\)-th moments a…
Breather gas and shielding for the focusing nonlinear Schrödinger equation with nonzero backgrounds
Weifang Weng, Guoqiang Zhang, Boris A. Malomed +1
Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \texti…
Long-time asymptotics for the -soliton solution to the KdV equation with two types of generalized reflection coefficients
Guoqiang Zhang, Zhenya Yan
We systematically investigate the long-time asymptotics for the -soliton solution to the KdV equation in the different regions with the aid of the Riemann-Hilbert (RH)…
Rigorous analysis of large-space and long-time asymptotics for the short-pulse soliton gases
Guoqiang Zhang, Weifang Weng, Zhenya Yan
We rigorously analyze the asymptotics of soliton gases to the short-pulse (SP) equation. The soliton gas is formulated in terms of a RH problem, which is derived from the RH proble…