### Abstract

The Bäcklund transformation for the three-level coupled Schrödinger-Maxwell equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of "binary solitons," a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.

Original language | English |
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Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 57 |

Issue number | 6 |

Publication status | Published - 1998 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*57*(6).

**Matched pulse propagation in a three-level system.** / Park, Q Han; Shin, H. J.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 57, no. 6.

}

TY - JOUR

T1 - Matched pulse propagation in a three-level system

AU - Park, Q Han

AU - Shin, H. J.

PY - 1998/12/1

Y1 - 1998/12/1

N2 - The Bäcklund transformation for the three-level coupled Schrödinger-Maxwell equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of "binary solitons," a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.

AB - The Bäcklund transformation for the three-level coupled Schrödinger-Maxwell equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant-electric-field background, we obtain a general solution for matched pulses (a pair of solitary waves) that can emit or absorb a light velocity solitary pulse but otherwise propagate with their shapes invariant. In the special case, this solution describes a steady-state pulse without emission or absorption, and becomes the matched pulse solution recently obtained by Hioe and Grobe [Phys. Rev. Lett. 73, 2559 (1994)]. A nonlinear superposition rule is derived from the Bäcklund transformation and used for the explicit construction of two solitons as well as non-Abelian breathers. Various features of these solutions are addressed. In particular, we analyze in detail the scattering of "binary solitons," a specific pair of different wavelength solitons, one of which moves with the velocity of light. Unlike the usual case of soliton scattering, the broader soliton changes its sign after the scattering, thus exhibiting a binary behavior. Surprisingly, the light velocity soliton receives a time advance through the scattering, thereby moving faster than light, which, however, does not violate causality.

UR - http://www.scopus.com/inward/record.url?scp=11744272210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11744272210&partnerID=8YFLogxK

M3 - Article

VL - 57

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

ER -