3 citations · 5 across the 12 of their papers we have counts for
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Long-time asymptotics of the integrable defocusing Wadati-Konno-Ichikawa equation with a finite-genus algebro-geometric background
Taohua Luo, Zhenya Yan, Guoqiang Zhang
We study the finite-genus algebro-geometric solutions of the Wadati-Konno-Ichikawa (WKI) equation with the saturable nonlinearity and long-time asymptotic behaviors of their short-…
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…
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…
On Large-Space and Long-Time Asymptotic Behaviors of Kink-Soliton Gases in the Sine-Gordon Equation
Guoqiang Zhang, Weifang Weng, Zhenya Yan
We conduct a comprehensive analysis of the large-space and long-time asymptotics of kink-soliton gases in the sine-Gordon (sG) equation, addressing an important open problem highli…
On the -soliton asymptotics for the modified Camassa-Holm equation with linear dispersion and vanishing boundaries
Weifang Weng, Zhenya Yan
We explore the -soliton asymptotics for the modified Camassa-Holm (mCH) equation with linear dispersion and boundaries vanishing at infinity: $m_t+(m(u^2-u_x^2)^2)_x+κu…
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…
The focusing complex mKdV equation with nonzero background: Large -order asymptotics of multi-rational solitons and related Painlevé-III hierarchy
Weifang Weng, Guoqiang Zhang, Zhenya Yan
In this paper, we investigate the large-order asymptotics of multi-rational solitons of the focusing complex modified Korteweg-de Vries (c-mKdV) equation with nonzero background vi…
Large-space and long-time asymptotic behaviors of -soliton solutions (soliton gas) for the focusing Hirota equation
Weifang Weng, Zhenya Yan
The Hirota equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation, and can describe the ultra-short optical pulse propagation in the form $…