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Nondegenerate and degenerate soliton solutions and their dynamics in two-component complex coupled integrable dispersionless equations

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  • Zhang, Bitong
  • Gao, Ben

Abstract

Novel N-soliton solutions of the two-component complex coupled integrable dispersionless (CID) equations are analytically constructed via the Hirota bilinear method, encompassing both nondegenerate forms and degenerate forms with bright–dark alternation properties. Numerical simulations reveal distinct types of soliton solutions. Specifically, nondegenerate solitons manifest as double-peaked structures, and degenerate solitons can exhibit characteristics of either conventional solitons or kink-solitons, depending on the parameters. On this basis, we conduct a detailed analysis of the soliton dynamics of the two-component complex CID equations and discuss the features and interactions of soliton solutions under different unit polarization vector and complex wave number parameters. Furthermore, the asymptotic analysis method is applied to study the interactions of degenerate and nondegenerate two-soliton solutions.

Suggested Citation

  • Zhang, Bitong & Gao, Ben, 2026. "Nondegenerate and degenerate soliton solutions and their dynamics in two-component complex coupled integrable dispersionless equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 154-174.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:154-174
    DOI: 10.1016/j.matcom.2026.01.031
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    References listed on IDEAS

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    1. Cai, Yue-Jin & Wu, Jian-Wen & Lin, Ji, 2022. "Nondegenerate N-soliton solutions for Manakov system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Manjit Singh & Shou-Fu Tian, 2023. "Lie symmetries, group classification and conserved quantities of dispersionless Manakov–Santini system in (2+1)-dimension," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 312-329, June.
    3. Li, Wentao & Li, Biao, 2024. "Construction of degenerate lump solutions for (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Cheng, Chong-Dong, 2023. "Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
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