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Numerical evaluations and asymptotic properties for the N-periodic wave solutions of an N=1 supersymmetric MKdV equation in fermionic field

Author

Listed:
  • Wen, Yanan
  • Zhao, Zhonglong
  • Xin, Pengcheng
  • Wang, Yu

Abstract

The N-periodic wave solutions of the N=1 supersymmetric modified Korteweg–de Vries (MKdV) equation are investigated by combining the super Hirota bilinear form and the super Riemann-theta function. The asymptotic behaviors of the quasi-periodic wave solutions as well as the relations between the quasi-periodic wave solutions and the soliton solutions are established and rigorously proved. The overdetermined system used to derive the N-periodic wave solutions can be converted into a least squares problem. By utilizing the global Levenberg–Marquardt (LM) method, the two- and above periodic wave solutions are obtained. This is the first time that the global LM method is used to solve the supersymmetric equation whose bilinear form with parity. The analytical method based on the characteristic lines is developed to analyze the dynamical characteristics of the N-periodic waves. In particular, based on the characteristic lines method, some dynamic characteristics including boundedness, periodicity, the analysis of the “influencing band” have been studied. In addition, quasi-periodic waves can exhibit a variety of patterns, such as parallel, crossed, and degenerated ones. Under the influence of Grassmann variable θ, the width of the “influencing band” shall increase as the amplitudes increase.

Suggested Citation

  • Wen, Yanan & Zhao, Zhonglong & Xin, Pengcheng & Wang, Yu, 2026. "Numerical evaluations and asymptotic properties for the N-periodic wave solutions of an N=1 supersymmetric MKdV equation in fermionic field," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:chsofr:v:203:y:2026:i:c:s0960077925016819
    DOI: 10.1016/j.chaos.2025.117668
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    References listed on IDEAS

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    1. Wen-Xiu Ma, 2025. "Matrix mKdV Integrable Hierarchies via Two Identical Group Reductions," Mathematics, MDPI, vol. 13(9), pages 1-10, April.
    2. Barak Freedman & Guy Bartal & Mordechai Segev & Ron Lifshitz & Demetrios N. Christodoulides & Jason W. Fleischer, 2006. "Wave and defect dynamics in nonlinear photonic quasicrystals," Nature, Nature, vol. 440(7088), pages 1166-1169, April.
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