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Algebraic solitons in the massive Thirring model.

Jiaqi Han1, Cheng He2, Dmitry E Pelinovsky1

  • 1Department of Mathematics and Statistics, <a href="https://ror.org/02fa3aq29">McMaster University</a>, Hamilton, Ontario, Canada L8S 4K1.

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We found exact solutions for two algebraic solitons in the massive Thirring model. A new double-soliton solution emerges from coalescing speeds, exhibiting double the mass and slow interaction.

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Area of Science:

  • Mathematical Physics
  • Soliton Theory
  • Quantum Field Theory

Background:

  • The massive Thirring model is a fundamental model in quantum field theory.
  • Solitons are stable, particle-like solutions to nonlinear partial differential equations.
  • Algebraic solitons represent a specific class of these solutions.

Purpose of the Study:

  • To derive exact solutions for the dynamics of two algebraic solitons in the massive Thirring model.
  • To investigate the properties of these solitons, including their mass and spectral characteristics.
  • To explore the formation and behavior of a double-soliton solution.

Main Methods:

  • Exact solution techniques for nonlinear systems.
  • Analysis of the Kaup-Newell spectral problem.
  • Investigating eigenvalue properties and soliton speeds.

Main Results:

  • Identified exact solutions for two algebraic solitons.
  • Each soliton corresponds to a simple embedded eigenvalue in the Kaup-Newell spectral problem.
  • A novel algebraic double-soliton solution was found by coalescing soliton speeds, corresponding to a double embedded eigenvalue and possessing double the mass of a single soliton.

Conclusions:

  • The derived double-soliton solution accurately describes the slow interaction of two identical algebraic solitons.
  • This work provides new insights into the complex dynamics of solitons in the massive Thirring model.