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arXiv · 2307.15136

Fokas-Lenells equation dark soliton and gauge equivalent spin equation

Riki Dutta·Sagardeep Talukdar·Gautam Kumar Saharia·Sudipta Nandy
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Abstract

We propose the Hirota bilinearization of the Fokas-Lenells derivative nonlinear Schrodinger equation with a non-vanishing background. The bilinear method is applied using an auxilary function to obtain the dark one soliton solution, dark two soliton solution and eventually the scheme for obtaining dark N soliton solutions. The use of auxilary function in bilinearization makes the method simpler than the ones reported earlier. Later, we have introduced a Lax pair for this integrable equation and using a transformation we have shown that this system is gauge equivalent to a spin system, namely the Landau-Lifshitz equation.

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Riki Dutta, Sagardeep Talukdar, Gautam Kumar Saharia, Sudipta Nandy. 2023-07-27. Fokas-Lenells equation dark soliton and gauge equivalent spin equation. https://arxiv.org/abs/2307.15136

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