Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

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

doi:10.1088/1751-8121/abb278

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $$\mathcal{PT}$$- and supersymmetric potential

Journal Article · Wed Oct 28 00:00:00 EDT 2020 · Journal of Physics. A, Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8121/abb278· OSTI ID:1840878

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

California Polytechnic State Univ., San Luis Obispo, CA (United States)
Univ. of New Hampshire, Durham, NH (United States)
The Santa Fe Inst., NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies (CNLS)
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 present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $$\mathcal{PT}$$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

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:: 1840878

Alternate ID(s):: OSTI ID: 23025663

Report Number(s):: LA-UR--20-22820

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 45 Vol. 53; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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