## Abstract

The number state method is used to study soliton bands for three anharmonic quantum lattices: (i) The discrete nonlinear Schrödinger equation, (ii) The Ablowitz-Ladik system, and (iii) A fermionic polaron model. Each of these systems is assumed to have f{hook}-fold translational symmetry in one spatial dimension, where f{hook} is the number of freedoms (lattice points). At the second quantum level (n = 2) we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy (E_{b}), effective mass (m^{*}) and maximum group velocity (V_{m}) of the soliton bands as functions of the anharmonicity in the limit f{hook} ? 8. For arbitrary values of n we have asymptotic expressions for E_{b}, m^{*}, and V_{ m} as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons. © 1994.

Original language | English |
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Pages (from-to) | 194-213 |

Number of pages | 20 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 78 |

Issue number | 3-4 |

Publication status | Published - 15 Nov 1994 |