Geodesic
On vector derivative nonlinear Schr\"odinger equation
Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 92-106

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We propose a sequence of Lax pairs, the compatibility conditions of which are integrable vector nonlinear equations. The first equations in this hierarchy are vector Kaup — Newell, Chen — Lee — Liu, Gerdjikov — Ivanov integrable nonlinear equations. The type of vector equation depends on an additional parameter $\alpha$. The proposed form of the vector Kaup — Newell equation has slight differences in comparison with the classical form. We show that the evolution of simplest nontrivial solutions of these equations is a composition of the evolutions of length and orientations of solution. We study properties of spectral curves of simplest nontrivial solutions the vector equations in the constructed hierarchy.
Keywords: integrable nonlinear equation, Kaup — Newell equation, Chen — Lee — Liu equation, multiphase equation, spectral curve.
Mots-clés : Gerdjikov — Ivanov equation 
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     title = {On vector derivative nonlinear {Schr\"odinger} equation},
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A. O. Smirnov; S. D. Shilovsky. On vector derivative nonlinear Schr\"odinger equation. Ufa mathematical journal, Tome 16 (2024) no. 3, pp. 92-106. http://geodesic.mathdoc.fr/item/UFA_2024_16_3_a7/