96 citations · 181 across the 14 of their papers we have counts for
14 papers
Massive Thirring Model: Inverse Scattering and Soliton Resolution
Cheng He, Jiaqi Liu, Changzheng Qu
In this paper the long-time dynamics of the massive Thirring model is investigated. Firstly the nonlinear steepest descent method for Riemann-Hilbert problem is explored to obtain…
Particle configurations for branching Brownian motion with an inhomogeneous branching rate
Jiaqi Liu, Jason Schweinsberg
Aiming to understand the distribution of fitness levels of individuals in a large population undergoing selection, we study the particle configurations of branching Brownian motion…
Long-time asymptotics and stability for the sine-Gordon equation
Gong Chen, Jiaqi Liu, Bingying Lu
In this paper, we study the long-time dynamics and stability properties of the sine-Gordon equation Firstly, we use the nonlinear steepest descent for R…
A Yaglom type asymptotic result for subcritical branching Brownian motion with absorption
Jiaqi Liu
We consider a slightly subcritical branching Brownian motion with absorption, where particles move as Brownian motions with drift , undergo dyadic fission a…
Soliton resolution for the modified KdV equation
Gong Chen, Jiaqi Liu
The soliton resolution for the focusing modified Korteweg-de vries (mKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on t…
The Derivative Nonlinear Schrödinger Equation: Global Well-Posedness and Soliton Resolution
Robert Jenkins, Jiaqi Liu, Peter Perry +1
We review recent results on global wellposedness and long-time behavior of smooth solutions to the derivative nonlinear Schrödinger (DNLS) equation. Using the integrable character…
Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces
Gong Chen, Jiaqi Liu
The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach…
-Sobolev space bijectivity of the inverse scattering of a AKNS system
Jiaqi Liu
We study the -Sobolev space bijectivity of the direct and inverse scattering of the AKNS system associated to the Manakov system and Sasa-Satsuma equation. We esta…
Global Existence for the Derivative Nonlinear Schrödinger Equation with Arbitrary Spectral Singularities
Robert Jenkins, Jiaqi Liu, Peter Perry +1
We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space . Our result exploits the complete integ…
Global Well-Posesedness for the Derivative Nonlinear Schrodinger Equation
Robert Jenkins, Jiaqi Liu, Peter Perry +1
We study the Derivative Nonlinear Schrödinger (DNLS). equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral sing…
Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
Robert Jenkins, Jiaqi Liu, Peter Perry +1
We study the Derivative Nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). D…
Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation
Robert Jenkins, Jiaqi Liu, Peter Perry +1
We study the Derivative Nonlinear Schrödinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but excluding spectral singularit…
Long-Time Behavior of Solutions to the Derivative Nonlinear Schrödinger Equation for Soliton-Free Initial Data
Jiaqi Liu, Peter Perry, Catherine Sulem
The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption tha…
Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
Jiaqi Liu, Peter Perry, Catherine Sulem
We develop inverse scattering for the derivative nonlinear Schrodinger equation (DNLS) on the line using its gauge equivalence with a related nonlinear dispersive equation. We prov…