General bright and dark soliton solutions to the massive Thirring model via KP hierarchy reductions

Chen, Junchao; Feng, Bao‐Feng

doi:10.48550/arxiv.2111.05718

Cited by 2 publications

(2 citation statements)

References 44 publications

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“…The connection between this model with other integrable models such as sine Gordon equation and derivative nonlinear Schrödinger equation has been discussed in the literature [11,25]. Recently, general bright and dark soliton solutions to BMTM has been obtained via KP hierarchy reductions [26]. Another interesting development in this context is the study of integrability of MTM in the presence of defect through inverse scattering transformation method [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

Basu-Mallick,

Sinha

2024

J. High Energ. Phys.

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A coupled bosonic massive Thirring model (BMTM), involving an interaction between the two independent spinors, is introduced and shown to be integrable. By incorporating suitable reductions between the field components of the coupled BMTM, five novel integrable models with various type of nonlocal interactions are constructed. Lax pairs satisfying the zero curvature condition are obtained for the coupled BMTM and for each of the related nonlocal models. An infinite number of conserved quantities are derived for each of these models which confirms the integrability of the systems. It is shown that the coupled BMTM respects important symmetries of the original BMTM such as parity, time reversal, global U(1)-gauge and the proper Lorentz transformations. Similarly, all the nonlocal models obtained from the coupled BMTM remain invariant under combined operation of parity and time reversal transformations. However, it is found that only one of the nonlocal models is invariant under proper Lorentz transformation and two other models are invariant under global U(1)-gauge transformation. By using ultralocal Poisson bracket relations among the elements of the Lax operator, it is shown that the coupled BMTM and one of the nonlocal models are completely integrable in the Liouville sense.

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Section: Introductionmentioning

confidence: 99%

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

Basu-Mallick,

Sinha

2024

J. High Energ. Phys.

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“…A great JHEP11(2023)018 deal of research has been devoted to the BMTM applying well-known techniques such as the inverse scattering transform, Bäcklund or Darboux transformations, and various types of soliton solutions and rogue waves thereof have been obtained [6,7,[16][17][18][19][20][21][22][23][24][25]. Further interesting results include the proof of the existence of soliton solutions in a nonvanishing background [26][27][28] and the construction of general bright and dark soliton solutions via KP hierarchy reductions [29], or the study of the integrability of the model in the presence of defects [30,31] and of balanced loss and gain [32].…”

Section: Introductionmentioning

confidence: 99%

Integrable coupled massive Thirring model with field values in a Grassmann algebra

Basu-Mallick,

Finkel,

González-López

et al. 2023

J. High Energ. Phys.

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A coupled massive Thirring model of two interacting Dirac spinors in 1 + 1 dimensions with fields taking values in a Grassmann algebra is introduced, which is closely related to a SU(1) version of the Grassmannian Thirring model also introduced in this work. The Lax pair for the system is constructed, and its equations of motion are obtained from a zero curvature condition. It is shown that the system possesses several infinite hierarchies of conserved quantities, which strongly confirms its integrability. The model admits a canonical formulation and is invariant under space-time translations, Lorentz boosts and global U(1) gauge transformations, as well as discrete symmetries like parity and time reversal. The conserved quantities associated to the continuous symmetries are derived using Noether’s theorem, and their relation to the lower-order integrals of motion is spelled out. New nonlocal integrable models are constructed through consistent nonlocal reductions between the field components of the general model. The Lagrangian, the Hamiltonian, the Lax pair and several infinite hierarchies of conserved quantities for each of these nonlocal models are obtained substituting its reduction in the expressions of the analogous quantities for the general model. It is shown that, although the Lorentz symmetry of the general model breaks down for its nonlocal reductions, these reductions remain invariant under parity, time reversal, global U(1) gauge transformations and space-time translations.

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General bright and dark soliton solutions to the massive Thirring model via KP hierarchy reductions

Cited by 2 publications

References 44 publications

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

Integrable coupled bosonic massive Thirring model and its nonlocal reductions

Integrable coupled massive Thirring model with field values in a Grassmann algebra

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