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Complex solitary waves and soliton trains in KdV and mKdV equations

Author

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  • Subhrajit Modak

    (Indian Institute of Science Education and Research Kolkata)

  • Akhil Pratap Singh

    (BITS Pilani, K.K. Birla Goa Campus)

  • Prasanta Kumar Panigrahi

    (Indian Institute of Science Education and Research Kolkata)

Abstract

We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.

Suggested Citation

  • Subhrajit Modak & Akhil Pratap Singh & Prasanta Kumar Panigrahi, 2016. "Complex solitary waves and soliton trains in KdV and mKdV equations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(6), pages 1-4, June.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:6:d:10.1140_epjb_e2016-70130-7
    DOI: 10.1140/epjb/e2016-70130-7
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    Statistical and Nonlinear Physics;

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