67 citations · 186 across the 24 of their papers we have counts for
24 papers
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…
Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation
Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang
In this work, we mainly study the general -soliton solutions of the nonlocal modified Korteweg-de Vries (mKdV) equation by utilizing the Riemann-Hilbert (RH) method. For the ini…
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 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…
Riemann-Hilbert approach to the inhomogeneous fifth-order nonlinear Schrödinger equation with non-vanishing boundary conditions
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
We consider the inhomogeneous fifth-order nonlinear Schrödinger (ifoNLS) equation with nonzero boundary condition in detailed. Firstly, the spectral analysis of the scattering prob…
A new matrix modified Korteweg-de Vries equation: Riemann-Hilbert approach and exact solutions
Wei-Kang Xun, Shou-Fu Tian, Jin-Jie Yang
A new matrix modified Korteweg-de Vries (mmKdV) equation with a complex-valued potential matrix function is first studied via Riemann-Hilbert approach, which can be red…
Riemann-Hilbert approach and -soliton solutions for a new four-component nonlinear Schrödinger equation
Xin-Mei Zhou, Shou-Fu Tian, Jin-Jie Yang +1
A new four-component nonlinear Schrödinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a $5\times…
Riemann-Hilbert approach and N-soliton solutions for the three-component coupled Hirota equations
Xin Wu, Shou-Fu Tian, Jin-Jie Yang
In this work, we consider an integrable three-component coupled Hirota (tcCH) equations in detail via the Riemann-Hilbert (RH) approach. We present some properties of the spectral…
Riemann-Hilbert approach and soliton solutions for the higher-order dispersive nonlinear Schrödinger equation with nonzero boundary conditions
Zhi-Qiang Li, Shou-Fu Tian, Jin-Jie Yang
In this work, the higher-order dispersive nonlinear Schrödinger equation with non-zero boundary conditions at infinity is investigated including the simple and double zeros of the…
Inverse scattering transform and soliton solutions for the focusing Kundu-Eckhaus equation with nonvanishing boundary conditions
Jin-Jie Yang, Shou-Fu Tian, Zhi-Qiang Li
The focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-H…
Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
Jin-Jie Yang, Shou-Fu Tian
We study systematically a matrix Riemann-Hilbert problem for the modified Landau-Lifshitz (mLL) equation with nonzero boundary conditions at infinity. Unlike the zero boundary cond…