Integrable negative flows of the Heisenberg ferromagnet equation hierarchy

  title={Integrable negative flows of the Heisenberg ferromagnet equation hierarchy},
  author={R. Ivanov},
  journal={The European Physical Journal Plus},
  • R. Ivanov
  • Published 1 June 2020
  • Physics
  • The European Physical Journal Plus
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 application of the dressing method is illustrated with the derivation of the one-soliton solution. 
2 Citations

EDITORIAL: “Solitons, Integrability, Nonlinear Waves: Theory and Applications”

1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria 2 Sankt-Petersburg State University of Aerospace Instrumentation, St-Petersburg, Russia 190000 3



Dark solitons of the Qiao's hierarchy

We obtain a class of soliton solutions of the integrable hierarchy which has been put forward in a series of works by Qiao. The soliton solutions are in the class of real functions approaching

On a novel integrable generalization of the nonlinear Schrödinger equation

We consider an integrable generalization of the nonlinear Schrödinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS

Smooth and peaked solitons of the CH equation

The relations between smooth and peaked soliton solutions are reviewed for the Camassa–Holm (CH) shallow water wave equation in one spatial dimension. The canonical Hamiltonian formulation of the CH

Generalizations of the Camassa–Holm equation

We classify generalized Camassa–Holm-type equations which possess infinite hierarchies of higher symmetries. We show that the obtained equations can be treated as negative flows of integrable

A new integrable equation with cuspons and W/M-shape-peaks solitons

In this paper, we propose a new completely integrable wave equation: mt+mx(u2−ux2)+2m2ux=0, m=u−uxx. The equation is derived from the two dimensional Euler equation and is proven to have Lax pair and

Integrable and non-integrable equations with peakons

We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new integrable equation first isolated by Degasperis

A New Integrable Equation with Peakon Solutions

We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa–Holm shallow

An integrable shallow water equation with peaked solitons.

  • CamassaHolm
  • Mathematics, Physics
    Physical review letters
  • 1993
We derive a new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by

Dressing Method for the Degasperis–Procesi Equation

The soliton solutions of the Degasperis–Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained