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arXiv · 1509.01712

Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations

Subhrajit Modak·Akhil P. Singh·P. K. Panigrahi
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Abstract

We demonstrate the existence of complex solitary wave and periodic solutions of the Kortweg de-vries (KdV) and modified Kortweg 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 ($\cal{P}$) and time-reversal ($\cal{T}$) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The $\cal{PT}$-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental $sech^2$ solution through supersymmetry.

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Subhrajit Modak, Akhil P. Singh, P. K. Panigrahi. 2015-09-05. Complex Solitary Waves and Soliton Trains in KdV and mKdV Equations. https://doi.org/10.1140/epjb%2Fe2016-70130-7

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