Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd-$\mathcal{PT}$ symmetry

Charalampidis, Efstathios G.; Cooper, Fred; Dawson, John F.; Khare, Avinash; Saxena, Avadh

doi:10.1088/1751-8121/abdca8

Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd-$$\mathcal{PT}$$ symmetry

Journal Article · Mon Mar 22 00:00:00 EDT 2021 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/abdca8· OSTI ID:1867175

^[1]; ^[2]; ^[3]; Khare, Avinash ^[4]; ^[5]

California Polytechnic State Univ., San Luis Obispo, CA (United States)
Santa Fe Inst. (SFI), Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
Univ. of New Hampshire, Durham, NH (United States)
Savitribai Phule Pune Univ., Pune (India)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)

In this work, we discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd-$$\mathcal{PT}$$ external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic $$\mathcal{PT}$$-symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1867175

Alternate ID(s):: OSTI ID: 23130967

Report Number(s):: LA-UR-20-26645

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 14 Vol. 54; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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