103 citations · 330 across the 34 of their papers we have counts for
35 papers
Soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space
Shou-Fu Tian, Tao Zhang
We prove the soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space . For a natural class o…
On long-time asymptotics to the nonlocal Lakshmanan -Porsezian-Daniel equation with step-like initial data
Wen-yu zhou, Shou-Fu Tian, Xiao-fan Zhang
In this work, the nonlinear steepest descent method is employed to study the long-time asymptotics of the integrable nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation with a step…
Characteristics of rogue waves in the scalar and vector nonlocal nonlinear Schrödinger equations
Xiu-Bin Wang, Shou-Fu Tian
In this paper, general higher-order rogue wave solutions of the parity-time () symmetric scalar and coupled nonlocal nonlinear Schrödinger equations (NLSE…
On the long-time asymptotic behavior of the Camassa-Holm equation in space-time solitonic regions
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, we are devoted to study the Cauchy problem of the Camassa-Holm (CH) equation with weighted Sobolev initial data in space-time solitonic regions \begin{align*} m_t+2κq…
On the long-time asymptotic of the modified Camassa-Holm equation with nonzero boundary conditions in space-time solitonic regions
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
We investigate the long-time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation with nonzero boundary conditions in different regions \begin{ali…
Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with finite density type initial data
Shou-Fu Tian, Zhi-Qiang Li, Jin-Jie Yang
In this work, we employ the -steepest descent method to investigate the Cauchy problem of the nonlocal nonlinear Schrödinger (NNLS) equation with finite density typ…
The long-time asymptotic behaviors of the solutions for the coupled dispersive AB system with weighted Sobolev initial data
Zi-Yi Wang, Shou-Fu Tian, Zhi-Qiang Li
In this work, we employ the -steepset descent method to study the Cauchy problem of the coupled dispersive AB system with initial conditions in weighted Sobolev spa…
Inverse scattering transform of the general coupled Hirota system with nonzero boundary conditions
Xiu-Bin Wang, Shou-Fu Tian
The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering tran…
Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data
Xin Wu, Shou-Fu Tian
In this work, we investigate the long-time asymptotic behavior of the Wadati-Konno-Ichikawa equation with initial data belonging to Schwartz space at infinity by using the nonlinea…
Soliton resolution for the Wadati-Konno-Ichikawa equation with weighted Sobolev initial data
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, we employ the -steepest descent method to investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with initial conditions in weight…
Long time asymptotic for the Wadati-Konno-Ichikawa equation with finite density initial data
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, we investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with finite density initial data. Employing the -generalization of Deift…
Inverse scattering transform and multiple high-order pole solutions for the nonlocal focusing and defocusing modified Korteweg-de Vries equation with the nonzero boundary conditions
Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang
We extend the Riemann-Hilbert (RH) method to study the inverse scattering transformation and high-order pole solutions of the focusing and defocusing nonlocal (reverse-space-time)…
On the asymptotic stability of -soliton solutions of the modified nonlinear Schrödinger equation
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
The Cauchy problem of the modified nonlinear Schrödinger (mNLS) equation with the finite density type initial data is investigated via steepest descent method…
Inverse scattering transform of the coupled modified Korteweg-de Vries equation with nonzero boundary conditions
Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang
In this work, we extend the Riemann-Hilbert (RH) method in order to study the coupled modified Korteweg-de Vries equation (cmKdV) under nonzero boundary conditions (NZBCs), and suc…
Riemann-Hilbert problem for the nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
The Riemann-Hilbert (RH) problem is first developed to study the focusing nonlinear Schrödinger (NLS) equation with multiple high-order poles under nonzero boundary conditions. Lau…
Soliton resolution for the complex short pulse equation with weighted Sobolev initial data
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
We employ the -steepest descent method in order to investigate the Cauchy problem of the complex short pulse (CSP) equation with initial conditions in weighted Sobo…
Soliton resolution for the Hirota equation with weighted Sobolev initial data
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
In this work, the steepest descent method is employed to investigate the soliton resolution for the Hirota equation with the initial value belong to weighted…
Soliton resolution for a coupled generalized nonlinear Schrödinger equations with weighted Sobolev initial data
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, we employ the steepest descent method in order to study the Cauchy problem of the cgNLS equations with initial conditions in weighted Sobolev space $…
Riemann-Hilbert problem for the sextic nonlinear Schrödinger equation with non-zero boundary conditions
Xin Wu, Shou-Fu Tian, Jin-Jie Yang +1
We consider a matrix Riemann-Hilbert problem for the sextic nonlinear Schrödinger equation with a non-zero boundary conditions at infinity. Before analyzing the spectrum problem, w…
Inverse scattering transform for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation
Wei-Kang Xun, Shou-Fu Tian
In this work, a generalized nonlocal Lakshmanan-Porsezian-Daniel (LPD) equation is introduced, and its integrability as an infinite dimensional Hamilton dynamic system is establish…
Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations
Wei-Kang Xun, Shou-Fu Tian
In this work, the generalized -component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for , are first investigat…
Inverse scattering transform and multi-solition solutions for the sextic nonlinear Schrödinger equation
Xin Wu, Shou-Fu Tian, Jin-Jie Yang
In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectrum problem are der…
Inverse scattering transform and soliton solutions for the modified matrix Korteweg-de Vries equation with nonzero boundary conditions
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
The theory of inverse scattering is developed to study the initial-value problem for the modified matrix Korteweg-de Vries (mmKdV) equation with the Lax pa…
Riemann-Hilbert approach to the generalized variable-coefficient nonlinear Schrödinger equation with non-vanishing boundary conditions
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, we consider the generalized variable-coefficient nonlinear Schrödinger equation with non-vanishing boundary conditions at infinity including the simple and double pol…