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<p>In this paper, the authors employ the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\bar{\partial}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mover> <mi mathvariant="normal">∂</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </math></EquationSource> </InlineEquation>-steepest descent method and Bäckhand transformation to investigate the asymptotic stability of Dirac solitons in the context of the massive Thirring model (MTM for short) system. They formulate the solution to the Cauchy problem for the MTM system in terms of the solution to a Riemann-Hilbert (RH for short) problem. This RH problem is decomposed into two components: A pure radiation solution and a soliton solution. As a direct outcome of this decomposition, they establish the asymptotic stability of Dirac solitons within the MTM system.</p>

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The Asymptotic Stability of Dirac Solitons in the Massive Thirring Model

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Ruihong Ma,
  • Engui Fan

摘要

In this paper, the authors employ the \(\bar{\partial}\) ∂ ¯ -steepest descent method and Bäckhand transformation to investigate the asymptotic stability of Dirac solitons in the context of the massive Thirring model (MTM for short) system. They formulate the solution to the Cauchy problem for the MTM system in terms of the solution to a Riemann-Hilbert (RH for short) problem. This RH problem is decomposed into two components: A pure radiation solution and a soliton solution. As a direct outcome of this decomposition, they establish the asymptotic stability of Dirac solitons within the MTM system.