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

Journal Article · Tue Oct 06 00:00:00 EDT 2015 · IEEE Journal of Selected Topics in Quantum Electronics

DOI:https://doi.org/10.1109/JSTQE.2015.2485607· OSTI ID:1234826

Cuevas-Maraver, Jesus ^[1]; Kevrekidis, Panayotis G. ^[2]; Saxena, Avadh ^[3]; Cooper, Fred ^[4]; Khare, Avinash ^[5]; Comech, Andrew ^[6]; Bender, Carl M. ^[7]

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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)

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: 14-50-00150; IRSES-605096; AC52-06NA25396
• OSTI ID: 1234826
• Report Number(s): LA-UR-15-26089
• Journal Information: IEEE Journal of Selected Topics in Quantum Electronics, Vol. 22, Issue 5; ISSN 1077-260X
• Publisher: IEEE Lasers and Electro-optics Society
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Analytical models
Eigenvalues and eigenfunctions
Mathematical model
Numerical models
Solitons
Stability analysis
Nonlinear dynamical systems
bifurcation
nonlinear differential equations