Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau-Lifschitz equation
arXiv:1910.07272 · doi:10.1088/1751-8121/ab81d9
Abstract
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.
arXiv comment22 pages, 4 figures
References in corpus (11)
- Nonlinear switching and solitons in PT-symmetric photonic systems
- Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems
- Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions
- Quantum nonlocality based on finite-speed causal influences leads to superluminal signaling
- Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
- Periodic and Hyperbolic Soliton Solutions of a Number of Nonlocal PT-Symmetric Nonlinear Equations
- Alice-Bob systems, -- principles and multi-soliton solutions
- Integrable nonlocal Hirota equations
- Nonlocal Fordy - Kulish Equations on Symmetric Spaces
- Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
- Effective Generation of Closed-form Soliton Solutions of the Continuous Classical Heisenberg Ferromagnet Equation