### Abstract

The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. If f --> infinity at a sufficiently small level of anharmonicity (gamma), the value for soliton binding energy from quantum field theory (QFT) in the continuum limit is recovered. For fixed f, however, the QFT result always fails for gamma sufficiently large and also for gamma sufficiently small. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.

Original language | English |
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Pages (from-to) | 509-516 |

Number of pages | 8 |

Journal | Physica Scripta T |

Volume | 44 |

Issue number | 6 |

Publication status | Published - Dec 1991 |

### Cite this

*Physica Scripta T*,

*44*(6), 509-516.

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*Physica Scripta T*, vol. 44, no. 6, pp. 509-516.

**BINDING-ENERGIES FOR DISCRETE NONLINEAR SCHRODINGER-EQUATIONS.** / Miller, P. D.; Scott, Alwyn C.; CARR, J ; Eilbeck, Chris.

Research output: Contribution to journal › Article

TY - JOUR

T1 - BINDING-ENERGIES FOR DISCRETE NONLINEAR SCHRODINGER-EQUATIONS

AU - Miller, P. D.

AU - Scott, Alwyn C.

AU - CARR, J

AU - Eilbeck, Chris

PY - 1991/12

Y1 - 1991/12

N2 - The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. If f --> infinity at a sufficiently small level of anharmonicity (gamma), the value for soliton binding energy from quantum field theory (QFT) in the continuum limit is recovered. For fixed f, however, the QFT result always fails for gamma sufficiently large and also for gamma sufficiently small. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.

AB - The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. If f --> infinity at a sufficiently small level of anharmonicity (gamma), the value for soliton binding energy from quantum field theory (QFT) in the continuum limit is recovered. For fixed f, however, the QFT result always fails for gamma sufficiently large and also for gamma sufficiently small. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.

M3 - Article

VL - 44

SP - 509

EP - 516

JO - Physica Scripta T

JF - Physica Scripta T

SN - 0281-1847

IS - 6

ER -