Mots-clés : solitons.
@article{TMF_2024_219_2_a5,
author = {J.-H. Chang},
title = {Parity{\textendash}time symmetric solitons of the~complex {KP} equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {274--286},
year = {2024},
volume = {219},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a5/}
}
J.-H. Chang. Parity–time symmetric solitons of the complex KP equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 274-286. http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a5/
[1] S. M. Alamoudi, U. Al Khawaja, B. B. Baizakov, “Averaged dynamics of soliton molecules in dispersion-managed optical fibers”, Phys. Rev. A, 89:5 (2014), 053817, 9 pp. | DOI
[2] A. Hasegawa, F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion”, Appl. Phys. Lett., 42:3 (1973), 142–144 | DOI
[3] L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fiber”, Phys. Rev. Lett., 45:13 (1980), 1095–1098 | DOI
[4] A. Hasegawa, Y. Kodama, Solitons in Optical Communications, Oxford Series in Optical and Imaging Sciences, 7, Clarendon Press, Oxford, 1995 | Zbl
[5] V. V. Konotop, J. Yang, D. A. Zezyulin, “Nonlinear waves in $\mathcal{PT}$-symmetric systems”, Rev. Mod. Phys., 88:3 (2016), 035002, 59 pp. | DOI
[6] S. V. Suchkov, A. A. Sukhorukov, J. Huang, S. V. Dmitriev, C. Lee, Yu. S. Kivshar, “Nonlinear switching and solitons in $PT$-symmetric photonic systems”, Laser Photonics Rev., 10:2 (2016), 177–213 | DOI
[7] C. M. Bender, S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having $\mathscr{P\!T}$ symmetry”, Phys. Rev. Lett., 80:24 (1998), 5243–5246 | DOI | MR
[8] E. P. Wigner, Group Theory and Its Application to Quantum Mechanics of Atomic Spectra, Pure and Applied Physics, 5, Academic Press, New York, 1959 | MR
[9] I. V. Barashenkov, D. A. Zezyulin, V. V. Konotop, “Exactly solvable Wadati potentials in the $PT$-symmetric Gross–Pitaevskii equation”, Pseudo-Hermitian Hamiltonians in Quantum Physics (Palermo, Italy, May 18–23, 2015), Springer Proceedings in Physics, 184, eds. F. Bagarello, R. Passante, C. Trapani, Springer, Cham, 2016, 143–156, arXiv: 1511.06633 | DOI
[10] A. A. Zyablovskii, A. P. Vinogradov, A. A. Pukhov, A. V. Dorofeenko, A. A. Lisyanskii, “PT-simmetriya v optike”, UFN, 184:11 (2014), 1177–1198 | DOI | DOI
[11] G. Biondini, S. Chakravarty, “Soliton solutions of the Kadomtsev–Petviashvili II equation”, J. Math. Phys., 47:3 (2006), 033514, 25 pp. | DOI | MR
[12] Y. Kodama, “KP solitons in shallow water”, J. Phys. A: Math. Theor., 43:43, 434004, 54 pp., arXiv: 1004.4607 | DOI | Zbl
[13] Y. Kodama, L. Williams, KP solitons and total positivity for the Grassmannian, arXiv: 1106.0023
[14] R. Hirota, The Direct Method in Soliton Theory, Cambridge Tracts in Mathematics, 155, eds. A. Nagai, J. Nimmo, C. Gilson, Cambridge Univ. Press, Cambridge, 2004 | DOI | MR | Zbl
[15] Y. Kodama, KP Solitons and the Grassmannians: Combinatorics and Geometry of Two-Dimensional Wave Patterns, SpringerBriefs in Mathematical Physics, 22, Springer, Singapore, 2017 | DOI | MR
[16] J. Cen, F. Correa, A. Fring, “Time-delay and reality conditions for complex solitons”, J. Math. Phys., 58:3 (2017), 032901 | DOI | MR
[17] F. Correa, A. Fring, “Regularized degenerate multi-solitons”, JHEP, 09 (2016), 008, 15 pp. | DOI | MR
[18] J. Cen, A. Fring, “Complex solitons with real energies”, J. Phys. A: Math. Theor., 49:36 (2016), 365202, 15 pp. | DOI | MR | Zbl
[19] G. Lévai, M. Znojil, “The interplay of supersymmetry and $\mathcal{PT}$ symmetry in quantum mechanics: a case study for the Scarf II potential”, J. Phys. A: Math. Gen., 35:41 (2002), 8793–8804 | DOI | MR
[20] S. Chakravarty, Y. Kodama, “A generating function for the $N$-soliton solutions of the Kadomtsev–Petviashvili II equation”, Special Functions and Orthogonal Polynomials, Contemporary Mathematics, 471, eds. D. Dominici, R. S. Maier, AMS, Providence, RI, 2008, 47–67 | DOI | MR
[21] P. Galashin, P. Pylyavskyy, “Ising model and the positive orthogonal Grassmannian”, Duke Math. J., 169:10 (2020), 1877–1942 | DOI | MR
[22] J.-H. Chang, Real line solitons of the BKP equation, arXiv: 2303.02385
[23] M. Wadati, “Construction of parity-time symmetric potential through the soliton theory”, J. Phys. Soc. Japan, 77:7 (2008), 074005, 4 pp. | DOI