982 citations · 2.9k across the 45 of their papers we have counts for
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The Riemann-Hilbert approach for the integrable fractional Fokas--Lenells equation
Ling An, Liming Ling
In this paper, we propose a new integrable fractional Fokas--Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering t…
Rogue waves and their patterns for the coupled Fokas-Lenells equations
Liming Ling, Huajie Su
In this work, we explore the rogue wave patterns in the coupled Fokas-Lenells equation by using the Darboux transformation. We demonstrate that when one of the internal parameters…
Elliptic-rogue waves and modulational instability in nonlinear soliton equations
Liming Ling, Xuan Sun
We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in theta functions. Unlike solutions generated on the plane wave background, these solutions dep…
Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation
Ling An, Liming Ling, Xiaoen Zhang
In this paper, we explore the integrable fractional derivative nonlinear Schrödinger (fDNLS) equation by using the inverse scattering transform. Firstly, we start from the recursio…
On the large-order asymtptics of Kuznetsov-Ma breathers
Liming Ling, Xiaoen Zhang
We study the large-order asymptotics for the Kuznetsov-Ma breather of the nonlinear Schrödinger equation in the far-field regime. With the aid of Darboux transformation, we first d…
Nondegenerate solitons in the integrable fractional coupled Hirota equation
Ling An, Liming Ling, Xiaoen Zhang
In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirot…
Large order breathers of the nonlinear Schrödinger equation
Liming Ling, Xiaoen Zhang
Multi-soliton and high-order soliton solutions are two type of famous ones in the integrable focusing nonlinear Schrödinger equation. The dynamics of multi-soliton was well known t…
The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
Liming Ling, Xuan Sun
We mainly construct and analyze the multi elliptic-localized solutions under the background of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equati…
Darboux transformation and solitonic solution to the coupled complex short pulse equation
Bao-Feng Feng, Liming Ling
The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact…
Stability of elliptic function solutions for the focusing modified KdV equation
Liming Ling, Xuan Sun
We study the spectral and orbital stability of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation and construct the corresponding breather solu…
Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
Jie-Yang Dong, Liming Ling, Xiaoen Zhang
The Kadomtsev-Petviashvili reduction method is a crucial method to derive the solitonic solutions of (1+1) dimensional integrable system from high dimensional system. In this work,…
Large and infinite order solitons of the coupled nonlinear Schrödinger equation
Liming Ling, Xiaoen Zhang
We study the large order and infinite order soliton of the coupled nonlinear Schrodinger equation with the Riemann-Hilbert method. By using the Riemann-Hilbert representation for t…
Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
Guoqiang Zhang, Liming Ling, Zhenya Yan +1
The extreme events are investigated for an -component nonlinear Schrödinger (-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields. We…
Asymptotic analysis of high order soliton for the Hirota equation
Xiaoen Zhang, Liming Ling
In this paper, we mainly analyze the long-time asymptotics of high-order soliton for the Hirota equation. Two different Riemann-Hilbert representations of Darboux matrix with high-…
A focusing and defocusing semi-discrete complex short pulse equation and its varioius soliton solutions
Bao-Feng Feng, Liming Ling, Zuonong Zhu
In this paper, we are concerned with a a semi-discrete complex short pulse (CSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz-…
Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
Deniz Bilman, Liming Ling, Peter D. Miller
We study the fundamental rogue wave solutions of the focusing nonlinear Schrödinger equation in the limit of large order. Using a recently-proposed Riemann-Hilbert representation o…
Collisional Dynamics of Solitons in the Coupled PT symmetric Nonlocal nonlinear Schrodinger equations
P. S. Vinayagam, R. Radha, U. Al Khawaja +1
We investigate the focusing coupled PT-symmetric nonlocal nonlinear Schrodinger equation employing Darboux transformation approach. We find a family of exact solutions including pa…
Modulational instability and homoclinic orbit solutions in vector nonlinear Schrödinger equation
Liming Ling, Li-Chen Zhao
Modulational instability has been used to explain the formation of breather and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain th…
General soliton solutions to a coupled Fokas-Lenells equation
Liming Ling, Bao-Feng Feng, Zuonong Zhu
In this paper, we firstly establish the multi-Hamiltonian structure and infinite many conservation laws for the vector Kaup-Newell hierarchy of the positive and negative orders. Th…
Multi-soliton, multi-breather and higher-order rogue wave solutions to the complex short pulse equation
Liming Ling, Bao-Feng Feng, Zuonong Zhu
In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid…
A defocusing complex short pulse equation and its multi-dark soliton solution by Darboux transformation
Bao-Feng Feng, Liming Ling, Zuonong Zhu
In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It…
Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations
Liming Ling, Li-Chen Zhao, Boling Guo
We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Schödinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classi…
Reply to "Comment on "Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations""
Liming Ling, Li-Chen Zhao, Boling Guo
In the recent comment quoted in the title (arXiv:1407.7852v1), a comment is presented on our recent work which derive a generalized nonlinear wave solution formula for mixed couple…
Darboux transformation and multi-dark soliton for N-component coupled nonlinear Schrödinger equations
Liming Ling, Li-Chen Zhao, Boling Guo
In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a dir…