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Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation
Abstract
This paper is the first part of a two-part study on the quantum nonlinear Schr\"odinger equation [the second paper follows: Lai and Haus, Phys. Rev. A 39, 854 (1989)]. The quantum nonlinear Schr\"odinger equation is solved analytically and is shown to have bound-state solutions. These bound-state solutions are closely related to the soliton phenomenon. This fact has not been pursued in the literature. In this paper we use the time-dependent Hartree approximation to construct approximate bound states and then superimpose these bound states to construct soliton states. This construction enables us to study the quantum effects of soliton propagation and soliton collisions.
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Citations
Cites
Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
Bethe, H. (1931) · Zeitschrift f�r Physik · doi:10.1007/bf01341708 · Cited by 3,768
Cited by
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Carusotto, I., & Ciuti, C. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.299 · Cited by 1,996
Scott, A. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90093-f · Cited by 656
Gruner, T., & Welsch, D.-G. (1996) · Physical Review A · doi:10.1103/physreva.53.1818 · Cited by 388
Dung, H. T., Knöll, L., & Welsch, D.-G. (1998) · Physical Review A · doi:10.1103/physreva.57.3931 · Cited by 371
Metadata
- Authors
- Lai, Y., & Haus, H. A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1989-07-01
- Volume
- 40
- Issue
- 2
- Pages
- 844-853
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2323363703
- Cited by
- 267
- References
- 1
- FWCI
- 7.47
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation. https://app.cochat.ai/papers/10.1103/physreva.40.844
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- Lai, Y., & Haus, H. A. (1989). Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation. Physical Review A. https://doi.org/10.1103/physreva.40.844
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