Coherent states as soliton solutions

B.V. Samsonov

L.-M. Duan, Guang‐Can Guo

Xie Yuan-Dong

An anisotropic Heisenberg ferromagnetic spin chain model is studied by using Holstain-Primakoff representation. In the semiclassical limit, the exact solutions for bright and dark solitons are found by using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. These results show that the solutions can be expressed in terms of the elliptic integrals in different parameter regions. Some solutions for dark solitons are the innovation points in this paper.

N. H. Christ, T. D. Lee

Hidetoshi Konno, Peter S. Lomdahl

The Wigner function, a kind of wavelet transform is studied for one- and two-soliton solutions to the nonlinear Schrödinger equation. The exact expression of the Wigner transform for the one-soliton solution is obtained. The features of soliton-soliton interaction of different two-soliton states, the states of coherence analogous to that of two-localized wave packets in quantum mechanics, are displayed. Suitability of this transform for analyzing “ soliton ” in open systems is also discussed.

Marek Cieplak, Łukasz A. Turski

Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.