Integrable negative flows of the Heisenberg ferromagnet equation hierarchy
arXiv:2201.02655 · doi:10.1140/epjp/s13360-020-00524-3
Abstract
We study the negative flows of the hierarchy of the integrable Heisenberg Ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We provide a framework which generates Lax pairs for the other members of the hierarchy. The Inverse scattering, based on the dressing method is illustrated with the derivation of the one-soliton solution.
arXiv comment13 pages, LaTeX
References in corpus (20)
- An integrable shallow water equation with peaked solitons
- Inverse Scattering Transform for the Camassa-Holm equation
- Multi-peakon solutions of the Degasperis-Procesi equation
- Multipeakons and a theorem of Stieltjes
- Ultra-short pulses in linear and nonlinear media
- On a novel integrable generalization of the nonlinear Schrödinger equation
- The Bi-Hamiltonian Structure of the Short Pulse Equation
- Inverse Scattering Transform for the Degasperis-Procesi Equation
- The N-soliton solution of the Degasperis-Procesi equation
- Complex short pulse and coupled complex short pulse equations
- A novel multi-component generalization of the short pulse equation and its multisoliton solutions
- Seiberg-Witten theory as a Fermi gas
- Multi-component generalizations of the {CH} equation: Geometrical Aspects, Peakons and Numerical Examples
- Dressing Method for the Degasperis-Procesi Equation
- Generalizations of the short pulse equation
- Smooth and Peaked Solitons of the CH equation
- Dark solitons of the Qiao's hierarchy
- Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation
- Riemann-Hilbert problem, integrability and reductions
- Camassa-Holm cuspons, solitons and their interactions via the dressing method