Abstract
In this paper, we consider the nonlinear Heisenberg Ferromagnetic chain equation
under Dirichlet boundary conditions. By Taylor formula, the nonlinear Heisenberg Ferromagnetic chain equation can be described by the nonlinear Schrödinger type equation. Using an infinite dimensional KAM theorem for reversible system, we prove the existence of many n-dimensional invariant tori under sufficiently small perturbation and thus many time quasi-periodic solutions for the above equation.
Notes
No potential conflict of interest was reported by the authors.
2 Here we only prove that the Heisenberg FM equation is not Hamiltonian with symplectic structure Maybe it is Hamiltonian with other symplectic form.