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Title: Solitary Waves of a $$\mathcal {P}$$ $$\mathcal {T}$$-Symmetric Nonlinear Dirac Equation

Abstract

In our study we consider we consider a prototypical example of a mathcalP mathcalT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the mathcalP mathcalT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the mathcalP mathcalT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the mathcalP mathcalT-transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of the model. Given the stability of the waveforms in the mathcalP mathcalT-exact phase, we consider them as initial conditions for parameters outside of that phase. We also find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding “quench”. The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU symmetry. Finally, we explore some special, analytically tractable, but not mathcalP mathcalT-symmetric solutions in the massless limit of t- e model.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [7]
+ Show Author Affiliations
  1. Univ. of Sevilla (Spain)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Santa Fe Inst. (SFI), Santa Fe, NM (United States)
  5. Savitribai Phule Pune Univ. (India)
  6. Texas A & M Univ., College Station, TX (United States); Russian Academy of Sciences (RAS), Moscow (Russian Federation). Inst. for Information Transmission Problems (IITP)
  7. Washington Univ., St. Louis, MO (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1234826
Report Number(s):
LA-UR-15-26089
Journal ID: ISSN 1077-260X
Grant/Contract Number:  
14-50-00150; IRSES-605096; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Journal of Selected Topics in Quantum Electronics
Additional Journal Information:
Journal Volume: 22; Journal Issue: 5; Journal ID: ISSN 1077-260X
Publisher:
IEEE Lasers and Electro-optics Society
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Analytical models; Eigenvalues and eigenfunctions; Mathematical model; Numerical models; Solitons; Stability analysis; Nonlinear dynamical systems; bifurcation; nonlinear differential equations

Citation Formats

Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., Saxena, Avadh, Cooper, Fred, Khare, Avinash, Comech, Andrew, and Bender, Carl M. Solitary Waves of a $\mathcal {P}$ $\mathcal {T}$-Symmetric Nonlinear Dirac Equation. United States: N. p., 2015. Web. doi:10.1109/JSTQE.2015.2485607.
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Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., Saxena, Avadh, Cooper, Fred, Khare, Avinash, Comech, Andrew, & Bender, Carl M. Solitary Waves of a $\mathcal {P}$ $\mathcal {T}$-Symmetric Nonlinear Dirac Equation. United States. https://doi.org/10.1109/JSTQE.2015.2485607
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Cuevas-Maraver, Jesus, Kevrekidis, Panayotis G., Saxena, Avadh, Cooper, Fred, Khare, Avinash, Comech, Andrew, and Bender, Carl M. Tue . "Solitary Waves of a $\mathcal {P}$ $\mathcal {T}$-Symmetric Nonlinear Dirac Equation". United States. https://doi.org/10.1109/JSTQE.2015.2485607. https://www.osti.gov/servlets/purl/1234826.
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@article{osti_1234826,
title = {Solitary Waves of a $\mathcal {P}$ $\mathcal {T}$-Symmetric Nonlinear Dirac Equation},
author = {Cuevas-Maraver, Jesus and Kevrekidis, Panayotis G. and Saxena, Avadh and Cooper, Fred and Khare, Avinash and Comech, Andrew and Bender, Carl M.},
abstractNote = {In our study we consider we consider a prototypical example of a mathcalP mathcalT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the mathcalP mathcalT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the mathcalP mathcalT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the mathcalP mathcalT-transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of the model. Given the stability of the waveforms in the mathcalP mathcalT-exact phase, we consider them as initial conditions for parameters outside of that phase. We also find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding “quench”. The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU symmetry. Finally, we explore some special, analytically tractable, but not mathcalP mathcalT-symmetric solutions in the massless limit of t- e model.},
doi = {10.1109/JSTQE.2015.2485607},
journal = {IEEE Journal of Selected Topics in Quantum Electronics},
number = 5,
volume = 22,
place = {United States},
year = {Tue Oct 06 00:00:00 EDT 2015},
month = {Tue Oct 06 00:00:00 EDT 2015}
}
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Journal Article:
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https://doi.org/10.1109/JSTQE.2015.2485607
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Works referencing / citing this record:

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