Complex solitary waves and soliton trains in KdV and mKdV equations

Subhrajit Modak, Akhil Pratap Singh and Prasanta Kumar Panigrahi ()
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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

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 6, 1-4

Abstract: 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.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-70130-7

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