Discrete mKdV Equation via Darboux Transformation


We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular discrete motion of discrete planar curves.


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The authors would like to thank Professor Udo Hertrich-Jeromin and the referees for valuable comments. The authors gratefully acknowledge the support from the JSPS/FWF Bilateral Joint Project I3809-N32 “Geometric shape generation” and JSPS Grants-in-Aid for: JSPS Fellows 19J10679, Scientific Research (C) 15K04845, (C) 20K03585 and (S) 17H06127 (P.I.: M.-H. Saito).


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Correspondence to Joseph Cho.

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Communicated by:Kenji Kajiwara

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Cho, J., Rossman, W. & Seno, T. Discrete mKdV Equation via Darboux Transformation. Math Phys Anal Geom 24, 25 (2021). https://doi.org/10.1007/s11040-021-09398-y

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  • mKdV equation
  • Discrete mKdV equation
  • Darboux transformations
  • Permutability
  • Transformation theory
  • Integrable systems

Mathematics Subject Classification (2020)

  • Primary 53A70
  • Secondary 35Q53
  • 53A04