Inverse Scattering for the Massive Thirring Model

DOI10.1007/978-1-4939-9806-7_11zbMath1442.35362arXiv1801.00039OpenAlexW2782262549MaRDI QIDQ5115063

Dmitry E. Pelinovsky, Aaron Saalmann

Publication date: 29 June 2020

Published in: Nonlinear Dispersive Partial Differential Equations and Inverse Scattering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.00039

zbMATH Keywords

general relativitymassive Thirring modelinverse scatteringRiemann-Hilbert approach

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Equations of motion in general relativity and gravitational theory (83C10) Riemann-Hilbert problems in context of PDEs (35Q15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (6)

Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces ⋮ Tau‐function formulation for bright, dark soliton and breather solutions to the massive Thirring model ⋮ Integrable coupled massive Thirring model with field values in a Grassmann algebra ⋮ Darboux transformation and soliton solutions of the semi-discrete massive Thirring model ⋮ The massive Thirring system in the quarter plane ⋮ Integrable semi-discretization of the massive Thirring system in laboratory coordinates

Cites Work

• Unnamed Item
• Global strong solution to the Thirring model in critical space
• Low regularity well-posedness for some nonlinear Dirac equations in one space dimension.
• Global existence for an \(L^2\) critical nonlinear Dirac equation in one dimension
• A soluble relativistic field theory
• Inverse scattering transform for systems with rational spectral dependence
• Long range scattering for the cubic Dirac equation on \(\mathbb{R}^{1+1}\).
• The derivative NLS equation: global existence with solitons
• Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
• Soliton resolution for the derivative nonlinear Schrödinger equation
• Global strong solution to a nonlinear Dirac type equation in one dimension
• Global solution to nonlinear Dirac equation for Gross-Neveu model in \(1+1\) dimensions
• Low regularity well-posedness for Gross-Neveu equations
• Global solutions to Gross-Neveu equation
• Orbital stability of Dirac solitons
• Evans function for Lax operators with algebraically decaying potentials
• L²orbital stability of Dirac solitons in the massive Thirring model
• Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering
• Survey on global existence in the nonlinear Dirac equations in one dimension
• The unified approach to integrable relativistic equations: Soliton solutions over nonvanishing backgrounds. II
• Stability of multi-solitons in the cubic NLS equation
• The DBAR Problem and the Thirring Model
• Scattering and inverse scattering for first order systems
• An exact solution for a derivative nonlinear Schrödinger equation
• L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
• Long-time asymptotics for the pure radiation solution of the sine—gordon equation
• Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
• Asymptotic stability of N-solitons in the cubic NLS equation
• Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method
• Global well-posedness for the derivative non-linear Schrödinger equation
• The asymptotic stability of solitons in the cubic NLS equation on the line

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