L2orbital stability of Dirac solitons in the massive Thirring model

DOI10.1080/03605302.2015.1123272zbMath1342.35287arXiv1312.1019OpenAlexW1626051177MaRDI QIDQ2810599

Dmitry E. Pelinovsky, Yusuke Shimabukuro, Andres Contreras

Publication date: 3 June 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1019

zbMATH Keywords

conserved quantitiesorbital stabilityLax operatorsauto-Bäcklund transformationmassive Thirring modelDirac solitons

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton equations (35Q51) PDEs in connection with relativity and gravitational theory (35Q75) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (13)

Transverse instability of line solitary waves in massive Dirac equations ⋮ On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential ⋮ Large time behavior of solution to nonlinear Dirac equation in \(1+1\) dimensions ⋮ Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field ⋮ Rogue waves in the massive Thirring model ⋮ Inverse Scattering for the Massive Thirring Model ⋮ Ill-posedness of the Thirring model below the critical regularity ⋮ Darboux transformation and soliton solutions of the semi-discrete massive Thirring model ⋮ Nonexistence of self-similar blowup for the nonlinear Dirac equations in \((1+1)\) dimensions ⋮ Compact implicit integration factor method for the nonlinear Dirac equation ⋮ On spectral stability of the nonlinear Dirac equation ⋮ Integrable semi-discretization of the massive Thirring system in laboratory coordinates ⋮ Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity

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