29 citations · 85 across the 11 of their papers we have counts for
11 papers
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…
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 $…
Well-posedness of scattering data for the derivative nonlinear Schrödinger equation in
Weifang Weng, Zhenya Yan
We prove the well-posedness results of scattering data for the derivative nonlinear Schrödinger equation in . We show that the reciprocal of the tr…
Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy
Minghe Zhang, Weifang Weng, Zhenya Yan
In this paper, we investigate the anomalous dispersive relations, inverse scattering transform with a Riemann-Hilbert (RH) problem, and fractional multi-solitons of the integrable…
Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations
Weifang Weng, Minghe Zhang, Zhenya Yan
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Sc…
Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes
Zijian Zhou, Li Wang, Weifang Weng +1
We introduce a deep neural network learning scheme to learn the Bäcklund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven solito…