One-dimensional optical solitons in cubic–quintic–septimal media with $$\varvec{\mathcal {PT}}$$PT-symmetric potentials
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-016-3138-x
Abstract: A ($$1+1$$1+1)-dimensional inhomogeneous cubic–quintic–septimal nonlinear Schrödinger equation with $$\mathcal {PT}$$PT-symmetric potentials is studied, and two families of soliton solutions are obtained. From soliton solutions, the amplitude of soliton is independent of the $$\mathcal {PT}$$PT-symmetric potential… read more here.
Keywords: cubic quintic; quintic septimal; dimensional optical; one dimensional ... See more keywords
Multi-soliton propagation in generalized inhomogeneous NLS equation with symmetric potentials
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DOI: 10.1016/j.ijleo.2018.12.186
Abstract: Abstract We investigate the generalized inhomogeneous NLS equation with symmetric potentials. Corresponding Lax pair is constructed through AKNS procedure. Based on the obtained Lax pair, one and two soliton solutions are generated via Darboux transformation… read more here.
Keywords: generalized inhomogeneous; symmetric potentials; equation symmetric; inhomogeneous nls ... See more keywords
Data driven soliton solution of the nonlinear Schrödinger equation with certain P T-symmetric potentials via deep learning.
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DOI: 10.1063/5.0086038
Abstract: We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schrödinger equation with parity time symmetric potentials. We consider three different parity time symmetric potentials, namely,… read more here.
Keywords: symmetric potentials; soliton solution; deep learning; equation ... See more keywords
Autonomous matter waves in two-component Bose–Einstein condensates with PT -symmetric potentials
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DOI: 10.1088/1402-4896/ae1b49
Abstract: The dynamics of autonomous matter waves in two-component Bose–Einstein condensates subject to PT -symmetric potentials are investigated within the framework of coupled Gross–Pitaevskii equations. Families of nonlinear modes are obtained through analytical and numerical methods,… read more here.
Keywords: matter waves; waves two; matter; autonomous matter ... See more keywords
Superoscillatory PT -symmetric potentials
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DOI: 10.1103/physreva.98.043830
Abstract: We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like potential always generates an entirely real… read more here.
Keywords: superoscillatory symmetric; symmetric potentials; symmetry;
Spectral singularities of odd- PT -symmetric potentials
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DOI: 10.1103/physreva.99.013823
Abstract: We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer matrix. The main… read more here.
Keywords: odd symmetric; singularities odd; transfer matrix; symmetric potentials ... See more keywords
Estimates for Eigenvalues of Sturm--Liouville Operators with some PT-Symmetric Potentials
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DOI: 10.15672/hujms.1542854
Abstract: We provide some useful equations for calculating the periodic and antiperiodic eigenvalues of the one-dimensional Schrödinger operator S(q) with a special potential that is a PT-symmetric trigonometric polynomial. We even give estimates to approximate complex… read more here.
Keywords: eigenvalues sturm; estimates eigenvalues; liouville operators; operators symmetric ... See more keywords