×

Rogue waves on the periodic background of the Kuralay-II equation. (English) Zbl 07881972

MSC:

35-XX Partial differential equations
76-XX Fluid mechanics
Full Text: DOI

References:

[1] Akhmediev, N.; Ankiewicz, A.; Taki, M., Waves that appear from nowhere and disappear without a trace, Phys. Lett. A, 373, 675-678, 2009 · Zbl 1227.76010
[2] Kharif, C.; Pelinovsky, E.; Slunyaev, A., Rogue Waves in the Ocean, 2009, Springer: Springer Heidelberg · Zbl 1230.86001
[3] Shats, M.; Punzmann, H.; Xia, H., Capillary rogue waves, Phys. Rev. Lett., 104, Article 104503 pp., 2010
[4] Bludov, Y. V.; Konotop, V. V.; Akhmediev, N., Matter rogue waves, Phys. Rev. A, 80, Article 033610 pp., 2009
[5] Solli, D. R.; Ropers, C.; Koonath, P.; Jalali, B., Optical rogue waves, Nature, 450, 1054-1057, 2007
[6] Peregrine, D. H., Water waves, nonlinear Schrödinger equations and their solutions, J. Austral. Math. Soc. 25, 16, 16-43, 1983 · Zbl 0526.76018
[7] Akhmediev, N.; Ankiewicz, A.; Soto-Crespo, J. M., Rogue waves and rational solutions of the nonlinear Schrödinger equation, Phys. Rev. E, 80, Article 026601 pp., 2009
[8] Wang, T. Y.; Qin, Z. Y.; Mu, G.; Zheng, F. Z., General high-order rogue waves in the Hirota equation, Appl. Math. Lett., 140, Article 108571 pp., 2023 · Zbl 1519.35279
[9] Chan, H. N.; Chow, K. W.; Kedziora, D. J.; Grimshaw, R. H.J.; Ding, E., Rogue wave modes for a derivative nonlinear Schrödinger model, Phys. Rev. E, 89, Article 032914 pp., 2014
[10] Liu, N.; Guo, B. L., Solitons and rogue waves of the quartic nonlinear Schrödinger equation by Riemann-Hilbert approach, Nonlinear Dynam., 100, 629-646, 2020 · Zbl 1434.35182
[11] Yan, X. W.; Tian, S. F.; Dong, M. J.; Zou, L., Bäcklund transformation, rogue wave solutions and interaction phenomena for a (3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation, Nonlinear Dynam., 92, 709-720, 2018 · Zbl 1398.37080
[12] Guo, B. L.; Ling, L. M.; Liu, Q. P., Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions, Phys. Rev. E, 85, Article 026607 pp., 2012
[13] Ji, J. L.; Yang, J.; Zhu, Z. N., Multi-soliton solutions for a nonlocal complex coupled dispersionless equation, Commun. Nonlinear Sci. Numer. Simul., 82, Article 105028 pp., 2020 · Zbl 1450.35114
[14] Wang, X.; He, J. S., Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation, Physica D, 446, Article 133639 pp., 2023 · Zbl 1510.35011
[15] Ye, R. S.; Zhang, Y., A vectorial Darboux transformation for the Fokas-Lenells system, Chaos Solitons Fractals, 169, Article 113233 pp., 2023
[16] Chen, J. B.; Pelinovsky, D. E., Rogue periodic waves in the focusing nonlinear Schrödinger equation, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 474, Article 20170814 pp., 2018 · Zbl 1402.35256
[17] Chen, J. B.; Pelinovsky, D. E.; White, R. E., Periodic standing waves in the focusing nonlinear Schrödinger equation: Rogue waves and modulation instability, Physica D, 405, Article 132378 pp., 2020 · Zbl 1490.35399
[18] Zhang, H. Q.; Chen, F., Rogue waves for the fourth-order nonlinear Schrödinger equation on the periodic background, Chaos, 31, Article 023129 pp., 2021 · Zbl 1467.35273
[19] Chen, J. B.; Pelinovsky, D. E., Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background, J. Nonlinear Sci., 29, 2797-2843, 2019 · Zbl 1427.35226
[20] Zhen, Y., Rogue waves on the periodic background in the complex modified KdV equation with higher-order effects, Wave Motion, Article 103209 pp., 2023 · Zbl 07825020
[21] Lou, L.; Zhang, Y.; Ye, R. S., Rogue waves on the general periodic traveling wave background for an extended modified Korteweg-de Vries equation, Math. Methods Appl. Sci., 44, 17, 13711-13722, 2021 · Zbl 1479.35723
[22] Peng, W. Q.; Tian, S. F.; Wang, X. B.; Zhang, T. T., Characteristics of rogue waves on a periodic background for the Hirota equation, Wave Motion, 93, Article 102454 pp., 2020 · Zbl 1524.35596
[23] Li, R. M.; Geng, X. G., Rogue periodic waves of the sine-Gordon equation, Appl. Math. Lett., 102, Article 106147 pp., 2020 · Zbl 1440.35030
[24] Chen, Y. X., Vector peregrine composites on the periodic background in spin-orbit coupled spin-1 Bose-Einstein condensates, Chaos, Solitons Fract., 169, Article 113251 pp., 2023
[25] Chen, J. B.; Pelinovsky, D. E., Periodic waves in the discrete mKdV equation: Modulational instability and rogue waves, Physica D, 445, Article 133652 pp., 2023 · Zbl 1509.35090
[26] Chen, J. B.; Pelinovsky, D. E., Rogue waves arising on the standing periodic waves in the Ablowitz-Ladik equation, 2023, arXiv:2303.17052
[27] Lakshmanan, M., Rigid body motions, space curves, prolongation structures, fiber bundles, and solitons, J. Math. Phys., 20, 8, 1667-1672, 1979 · Zbl 0416.70016
[28] Myrzakulova, Z.; Nugmanova, G.; Yesmakhanova, K.; Serikbayev, N.; Myrzakulov, R., Integrable generalized heisenberg ferromagnet equations with self-consistent potentials and related Yajima-Oikawa type equations, 2022, arXiv:2207.13520
[29] Sagidullayeva, Z.; Nugmanova, G.; Myrzakulov, R.; Serikbayev, N., Integrable kuralay equations: Geometry, solutions and generalizations, Symmetry, 14, 1374, 2022
[30] Yang, Q. Q.; Li, C. Z., Darboux transformation and soliton solutions of the nonlocal heisenberg spin system with self-consistent potential, Int. J. Geom. Methods M., 20, 07, Article 2350123 pp., 2023 · Zbl 1535.37089
[31] Kong, H. Y.; Guo, R., Breathers, rogue waves and semi-rational solutions for a heisenberg ferromagnet-type equation, Mod. Phys. Lett. B, 37, 20, Article 2350053 pp., 2023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.