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arXiv · 2211.13791

Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation

Bjorn K. Berntson·Edwin Langmann·Jonatan Lenells
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Abstract

We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These solutions are obtained by a spin-pole ansatz including a dynamical background term; we show that this ansatz solves the periodic sncILW equation provided the spins and poles satisfy the elliptic $A$-type spin Calogero-Moser (sCM) system with certain constraints on the initial conditions. The key to this result is a B\"{a}cklund transformation for the elliptic sCM system which includes a non-trivial dynamical background term. We also present solutions of the sncILW equation on the real line and of the spin Benjamin-Ono equation which generalize previously obtained solutions by allowing for a non-trivial background term.

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Bjorn K. Berntson, Edwin Langmann, Jonatan Lenells. 2022-11-24. Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation. https://doi.org/10.1007/s11005-023-01681-z

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