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arXiv · 2301.07225

NLS-type equations from quadratic pencil of Lax operators: negative flows

Rossen I. Ivanov
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Abstract

We formulate and study an integrable model of Nonlinear Schr\"odinger (NLS)-type through its Lax representation, where one of the Lax operators is quadratic and the other has a rational dependence on the spectral parameter. We discuss the associated spectral problem, the Riemann-Hilbert problem formulation, the conserved quantities, as well as a generalisation for symmetric spaces. In addition we explore the possibilities for modelling with higher order NLS (HNLS) integrable equations and in particular, the relevance of the proposed system.

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Rossen I. Ivanov. 2023-01-17. NLS-type equations from quadratic pencil of Lax operators: negative flows. https://doi.org/10.1016/j.chaos.2022.112299

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