Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau-Lifschitz equation

We exploit the gauge equivalence between the Hirota equation and the extended continuous Heisenberg equation to investigate how nonlocality properties of one system are inherited by the other. We provide closed generic expressions for nonlocal multi-soliton solutions for both systems. By demonstrati...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-05, Vol.53 (19), p.195201
Main Authors: Cen, Julia, Correa, Francisco, Fring, Andreas
Format: Article
Language:English
Subjects:
Darboux transformations
Hirota equation
Landau-Lifschitz equation
multi-soliton solutions
PT-symmetry
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Summary:We exploit the gauge equivalence between the Hirota equation and the extended continuous Heisenberg equation to investigate how nonlocality properties of one system are inherited by the other. We provide closed generic expressions for nonlocal multi-soliton solutions for both systems. By demonstrating that a specific auto-gauge transformation for the extended continuous Heisenberg equation becomes equivalent to a Darboux transformation, we use the latter to construct the nonlocal multi-soliton solutions from which the corresponding nonlocal solutions to the Hirota equation can be computed directly. We discuss properties and solutions of a nonlocal version of the nonlocal extended Landau-Lifschitz equation obtained from the nonlocal extended continuous Heisenberg equation or directly from the nonlocal solutions of the Hirota equation.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab81d9