Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
-
Zhe Gao
,
Chuan-Qi Su
Abstract
Under investigation in this article is a generalised nonlinear Schrödinger-Maxwell-Bloch system for the picosecond optical pulse propagation in an inhomogeneous erbium-doped silica optical fibre. Lax pair, conservation laws, Darboux transformation, and generalised Darboux transformation for the system are constructed; with the one- and two-soliton solutions, the first- and second-order rogue waves given. Soliton propagation is discussed. Nonlinear tunneling effect on the solitons and rogue waves are investigated. We find that (i) the detuning of the atomic transition frequency from the optical pulse frequency affects the velocity of the pulse when the detuning is small, (ii) nonlinear tunneling effect does not affect the energy redistribution of the soliton interaction, (iii) dispersion barrier/well has an effect on the soliton velocity, whereas nonlinear well/barrier does not, (iv) nonlinear well/barrier could amplify/compress the solitons or rogue waves in a smoother manner than the dispersion barrier/well, and (v) dispersion barrier could “attract” the nearby rogue waves, whereas the dispersion well has a repulsive effect on them.
Acknowledgments
We express our sincere thanks to the editors, referees, and all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11272023 and by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) under Grant No. IPOC2013B008.
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©2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
- Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
- Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
- Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
- Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
- Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
- Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
- Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
- Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
- The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
- Rapid Communication
- Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
Artikel in diesem Heft
- Frontmatter
- Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
- Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
- Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
- Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
- Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
- Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
- Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
- Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
- Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
- The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
- Rapid Communication
- Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
