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PT-symmetric solitons and parameter discovery in self-defocusing saturable nonlinear Schrödinger equation via LrD-PINN. (English) Zbl 07859775


MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
68T05 Learning and adaptive systems in artificial intelligence
68T07 Artificial neural networks and deep learning
Full Text: DOI

References:

[1] Bender, C. M.; Boettcher, S., Real spectra in Non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett., 80, 5243-5246 (1998) · Zbl 0947.81018 · doi:10.1103/PhysRevLett.80.5243
[2] Qi, B.; Chen, H. Z.; Ge, L.; Berini, P.; Ma, R. M., Parity-time symmetry synthetic lasers: Physics and devices, Adv. Opt. Mater., 7, 1900694 (2019) · doi:10.1002/adom.201900694
[3] Bo, W. B.; Wang, R. R.; Fang, Y.; Wang, Y. Y.; Dai, C. Q., Prediction and dynamical evolution of multipole soliton families in fractional Schrödinger equation with the PT-symmetric potential and saturable nonlinearity, Nonlinear Dyn., 111, 1577-1588 (2023) · doi:10.1007/s11071-022-07884-8
[4] Yu, F. J., Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential, Chaos, 27, 023108 (2017) · Zbl 1390.35345 · doi:10.1063/1.4975763
[5] Yang, X.; Li, J. W.; Ding, Y. F.; Xu, M. W.; Zhu, X. F.; Zhu, J., Observation of transient parity-time symmetry in electronic systems, Phys. Rev. Lett., 128, 065701 (2022) · doi:10.1103/PhysRevLett.128.065701
[6] Hejazi, S. S. S.; Polo, J.; Sachdeva, R.; Busch, T., Symmetry breaking in binary Bose-Einstein condensates in the presence of an inhomogeneous artificial gauge field, Phys. Rev. A., 102, 053309 (2020) · doi:10.1103/PhysRevA.102.053309
[7] Kanasugi, S.; Yanase, Y., Anapole superconductivity from PT \(\operatorname{\smallsetminus}\) documentclass-symmetric mixed-parity interband pairing, Commun. Phys., 5, 39 (2022) · doi:10.1038/s42005-022-00804-7
[8] El-Ganainy, R.; Makris, K. G.; Christodoulides, D. N.; Musslimani, Z. H., Theory of coupled optical PT-symmetric structures, Opt. Lett., 32, 17, 2632-2634 (2007) · doi:10.1364/OL.32.002632
[9] Nixon, S.; Yang, J. K., Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides, Opt. Lett., 41, 2747-2750 (2016) · doi:10.1364/OL.41.002747
[10] Nath, D.; Gao, Y. L.; Mareeswaran, R. B.; Kanna, T.; Roy, B., Bright-dark and dark-dark solitons in coupled nonlinear Schrodinger equation with PT-symmetric potentials, Chaos, 27, 123102 (2017) · Zbl 1390.35337 · doi:10.1063/1.4997534
[11] Yang, J. K., Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials, Opt. Lett., 39, 5547-5550 (2014) · doi:10.1364/OL.39.005547
[12] Dai, C. Q.; Wang, X. G., Light bullet in parity-time symmetric potential, Nonlinear Dyn., 77, 1133-1139 (2014) · doi:10.1007/s11071-014-1365-6
[13] Suchkov, S. V.; Churkin, D. V.; Sukhorukov, A. A., Nonlinear transition between PT-symmetric and PT-broken modes in coupled fiber lasers, Opt. Express, 28, 30340-30348 (2020) · doi:10.1364/OE.397853
[14] Pardell, J. M.; Herrero, R.; Botey, M.; Staliunas, K., Stabilized narrow-beam emission from broad-area semiconductor lasers, Phys. Rev. A, 101, 033833 (2020) · doi:10.1103/PhysRevA.101.033833
[15] Özdemir, S. K.; Rotter, S.; Nori, F.; Yang, L., Parity-time symmetry and exceptional points in photonics, Nat. Mater., 18, 783-798 (2019) · doi:10.1038/s41563-019-0304-9
[16] Liang, H. X.; Dai, Y. H.; Shu, S. J.; Xu, S. L.; Wang, K. S.; Ai, Y., Two dimension PT symmetry spacial soliton in atomic gases with linear and nonlinear potentials, Optik, 213, 164705 (2020) · doi:10.1016/j.ijleo.2020.164705
[17] Xu, Z. H.; Chen, S., Dynamical evolution in a one-dimensional incommensurate lattice with PT symmetry, Phys. Rev. A, 103, 043325 (2021) · doi:10.1103/PhysRevA.103.043325
[18] Longhi, S., Quantum statistical signature of PT symmetry breaking, Opt. Lett., 45, 1591-1594 (2020) · doi:10.1364/OL.386232
[19] Barashenkov, I. V.; Smuts, F.; Chernyavsky, A., Integrability and trajectory confinement in -symmetric waveguide arrays, J. Phys. A Math. Theor., 56, 165701 (2023) · Zbl 1512.78023 · doi:10.1088/1751-8121/acc3ce
[20] Alexeeva, N. V.; Barashenkov, I. V.; Saxena, A., Spinor solitons and their PT-symmetric offspring, Ann. Phys., 403, 198-223 (2019) · Zbl 1411.81114 · doi:10.1016/j.aop.2018.11.010
[21] Chen, Y.; Yan, Z. Y.; Mihalache, D., Soliton formation and stability under the interplay between parity-time-symmetric generalized scarf-II potentials and kerr nonlinearity, Phys. Rev. E., 102, 012216 (2020) · doi:10.1103/PhysRevE.102.012216
[22] Bo, W. B.; Wang, R. R.; Liu, W.; Wang, Y. Y., Symmetry breaking of solitons in the PT-symmetric nonlinear schrodinger equation with the cubic-quintic competing saturable nonlinearity, Chaos, 32, 093104 (2022) · Zbl 1541.35123 · doi:10.1063/5.0091738
[23] Akramov, M. E.; Yusupov, J. R.; Ehrhardt, M.; Susanto, H.; Matrasulov, D. U., Transparent boundary conditions for the nonlocal nonlinear Schrodinger equation: A model for reflectionless propagation of PT-symmetric solitons, Phys. Lett. A, 459, 128611 (2023) · Zbl 1524.35575 · doi:10.1016/j.physleta.2022.128611
[24] Zhou, Z. J.; Song, J.; Weng, W. F.; Yan, Z. Y., Stable solitons and interactions of the logarithmic nonlinear Schrodinger equation with two PT-symmetric non-periodic potentials, Appl. Math. Lett., 132, 108131 (2022) · Zbl 1497.81054 · doi:10.1016/j.aml.2022.108131
[25] Hanif, Y.; Saleem, U., Degenerate and non-degenerate solutions of PT-symmetric nonlocal integrable discrete nonlinear Schrodinger equation, Phys. Lett. A, 384, 126834 (2020) · Zbl 1448.35471 · doi:10.1016/j.physleta.2020.126834
[26] Su, W. W.; Deng, H. Y.; Dong, L. W.; Huang, Z. F.; Huang, C. M., Stabilization of fundamental solitons in the nonlinear fractional Schrodinger equation with PT-symmetric nonlinear lattices, Chaos Solitons Fractals, 141, 110427 (2020) · Zbl 1496.35439 · doi:10.1016/j.chaos.2020.110427
[27] Sene, N., Analytical solutions of Hristov diffusion equations with non-singular fractional derivatives, Chaos, 29, 023112 (2019) · Zbl 1409.35228 · doi:10.1063/1.5082645
[28] Attipoe, D. S.; Tambue, A., Convergence of the mimetic finite difference and fitted mimetic finite difference method for options pricing, Appl. Math. Comput., 401, 126060 (2021) · Zbl 1508.91612 · doi:10.1016/j.amc.2021.126060
[29] Li, X.; Wang, L.; Zhou, Z. J.; Chen, Y.; Yan, Z. Y., Stable dynamics and excitations of single- and double-hump solitons in the kerr nonlinear media with PT-symmetric HHG potentials, Nonlinear Dyn., 108, 4045-4056 (2022) · doi:10.1007/s11071-022-07362-1
[30] Kihm, K. D.; Lyons, D. P., Optical tomography using a genetic algorithm, Opt. Lett., 21, 1327-1329 (1996) · doi:10.1364/OL.21.001327
[31] Martin, S.; Rivory, J.; Schoenauer, M., Synthesis of optical multilayer systems using genetic algorithms, Appl. Opt., 34, 2247-2254 (1995) · doi:10.1364/AO.34.002247
[32] Zhu, B. W.; Fang, Y.; Liu, W.; Dai, C. Q., Predicting the dynamic process and model parameters of vector optical solitons under coupled higher-order effects via WL-tsPINN, Chaos Solitons Fractals, 162, 112441 (2022) · doi:10.1016/j.chaos.2022.112441
[33] Zhang, Y. B.; Liu, H. Y.; Wang, L.; Sun, W. R., The line rogue wave solutions of the nonlocal Davey-Stewartson I equation with PT symmetry based on the improved physics-informed neural network, Chaos, 33, 013118 (2023) · Zbl 07880560 · doi:10.1063/5.0102741
[34] Fang, Y.; Wu, G. Z.; Kudryashov, N. A.; Wang, Y. Y.; Dai, C. Q., Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method, Chaos Solitons Fractals, 158, 112118 (2022) · Zbl 1505.35316 · doi:10.1016/j.chaos.2022.112118
[35] Lin, S.; Chen, Y., Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions, Physica D, 445, 133629 (2023) · Zbl 07653434 · doi:10.1016/j.physd.2022.133629
[36] Wang, L.; Yan, Z. Y., Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrodinger equation with a potential using the PINN deep learning, Phys. Lett. A, 404, 127408 (2021) · Zbl 07409914 · doi:10.1016/j.physleta.2021.127408
[37] Jiang, X.; Wang, D.; Fan, Q.; Zhang, M.; Lu, C.; Lau, A. P. T., Physics-informed neural network for nonlinear dynamics in fiber optics, Laser Photonics Rev., 16, 2100483 (2022) · doi:10.1002/lpor.202100483
[38] Raissi, M.; Perdikaris, P.; Karniadakis, G. E., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686-707 (2019) · Zbl 1415.68175 · doi:10.1016/j.jcp.2018.10.045
[39] Hu, Y.; Bai, Y.; Liu, Y.; Ding, S. L.; Hua, S. Y.; Jiang, X. S.; Xiao, M., Absorption and gain saturable nonlinearities in erbium-doped optical microcavities, Phys. Rev. A, 100, 033831 (2019) · doi:10.1103/PhysRevA.100.033831
[40] Barashenkov, I. V.; Zezyulin, D. A.; Konotop, V. V., Exactly solvable Wadati potentials in the PT-symmetric gross-Pitaevskii equation, Spring Proc. Phys., 184, 143-155 (2016) · Zbl 1402.81126 · doi:10.1007/978-3-319-31356-6
[41] Li, X. J.; Liao, J. L.; Nie, Y. M.; Marko, M.; Jia, H.; Liu, J.; Wang, X. C.; Wong, C. W., Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG, Opt. Express, 23, 10282-10292 (2015) · doi:10.1364/OE.23.010282
[42] Horikis, T. P.; Frantzeskakis, D. J., Vector nematicons: Coupled spatial solitons in nematic liquid crystals, Phys. Rev. A, 94, 053805 (2016) · doi:10.1103/PhysRevA.94.053805
[43] Li, P. F.; Dai, C. Q.; Li, R. J.; Gao, Y. Q., Symmetric and asymmetric solitons supported by a PT-symmetric potential with saturable nonlinearity: Bifurcation, stability and dynamics, Opt. Express, 26, 6949-6961 (2018) · doi:10.1364/OE.26.006949
[44] Guo, D. C.; Xiao, J.; Gu, L. L.; Jin, H. Z.; Dong, L. W., One- and two-dimensional bright solitons in inhomogeneous defocusing nonlinearities with an antisymmetric periodic gain and loss, Physica D, 343, 1-6 (2017) · Zbl 1378.35278 · doi:10.1016/j.physd.2016.11.005
[45] Sudharsan, J. B.; Manikandan, K.; Aravinthan, D., Stabilization of solitons in collisionally inhomogeneous higher-order nonlinear media with PT-symmetric harmonic-Gaussian potential with unbounded gain-loss distributions, Eur. Phys. J. Plus, 137, 860 (2022) · doi:10.1140/epjp/s13360-022-03081-z
[46] Barashenkov, I. V.; Zezyulin, D. A.; Konotop, V. V., Jamming anomaly in-symmetric systems, N. J. Phys., 18, 075015 (2016) · doi:10.1088/1367-2630/18/7/075015
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