Gap solitons and Bloch waves in nonlinear periodic systems

Journal Article · Tue Dec 15 04:00:00 EST 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.063815· OSTI ID:21352434

Yongping, Zhang; Biao, Wu ^[1]; Zhaoxin, Liang ^[2]

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1. Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Wenhua Road 72, Shenyang 110016 (China)

We comprehensively investigate gap solitons and Bloch waves in one-dimensional nonlinear periodic systems. Our results show that there exists a composition relation between them: Bloch waves at either the center or edge of the Brillouin zone are infinite chains composed of fundamental gap solitons (FGSs). We argue that such a relation is related to the exact relation between nonlinear Bloch waves and nonlinear Wannier functions. With this composition relation, many conclusions can be drawn for gap solitons without any computation. For example, for the defocusing nonlinearity, there are n families of FGS in the nth linear Bloch band gap; for the focusing case, there are infinite number of families of FGSs in the semi-infinite gap and other gaps. In addition, the stability of gap solitons is analyzed. In literature, there are numerical results showing that some FGSs have cutoffs on propagation constant (or chemical potential), i.e., these FGSs do not exist for all values of propagation constant (or chemical potential) in the linear band gap. We develop an intuitive picture to describe this cutoff.

• OSTI ID: 21352434
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BRILLOUIN ZONES
CALCULATION METHODS
FOCUSING
FUNCTIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PERIODIC SYSTEM
POTENTIALS
QUASI PARTICLES
SOLITONS
STABILITY
ZONES