Cụm sóng lừa Kuznetsov–Ma của phương trình Schrödinger phi tuyến
Tóm tắt
Trong công trình này, chúng tôi điều tra các cụm sóng lừa (RW) có hình dạng khác nhau, bao gồm các soliton Kuznetsov–Ma (KMS) từ phương trình Schrödinger phi tuyến (NLSE) với phi tuyến Kerr. Chúng tôi trình bày ba loại nghiệm chính xác bậc cao trên nền tảng đồng nhất được tính toán bằng cách sử dụng phương pháp biến đổi Darboux (DT) với các tham số được chọn một cách chính xác. Phân lớp nghiệm đầu tiên có đặc trưng là các đỉnh cường độ mạnh và hẹp được lặp lại dọc theo trục tiến hóa
Từ khóa
Tài liệu tham khảo
Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., Biswas, A., Belić, M.: Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81, 1933–1349 (2015)
Khalique, C.M.: Stationary solutions for nonlinear dispersive Schroödinger equation. Nonlinear Dyn. 63, 623–626 (2011)
Agrawal, G.P.: Applications of Nonlinear Fiber Optics. Academic Press, San Diego (2001)
Kivshar, Y.S., Agrawal, G.P.: Optical Solitons. Academic Press, San Diego (2003)
Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: Observation of Kuznetsov-Ma soliton dynamics in optical fibre. Sci. Rep. 6, 463 (2012)
Bao, W.: The nonlinear Schrödinger equation and applications in Bose-Einstein condensation and plasma physics. In: Lecture Note Series, IMS, NUS, vol. 9 (2007)
Busch, T., Anglin, J.R.: Dark-bright solitons in inhomogeneous Bose-Einstein condensates. Phys. Rev. Lett. 87, 010401 (2001)
Dudley, J.M., Genty, G., Mussot, A., Chabchoub, A., Dias, F.: Rogue waves and analogies in optics and oceanography. Nat. Rev. Phys. 1, 675–689 (2019)
Zakharov, V.E.: Stability of periodic waves of finite amplitude on a surface of deep fluid. J. Appl. Mech. Tech. Phys. 9 (1968)
Osborne, A.: Nonlinear Ocean Waves and the Inverse Scattering Transform. Academic Press, London (2010)
Ankiewicz, A., Kedziora, D.J., Chowdury, A., Bandelow, U., Akhmediev, N.: Infinite hierarchy of nonlinear Schrödinger equations and their solutions. Phys. Rev. E 93, 012206 (2016)
Kedziora, D.J., Ankiewicz, A., Chowdury, A., Akhmediev, N.: Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients. Chaos 25, 103114 (2015)
Mani Rajan, M.S., Mahalingam, A.: Nonautonomous solitons in modified inhomogeneous Hirota equation: soliton control and soliton interaction. Nonlinear Dyn. 79, 2469–2484 (2015)
Wang, D.-S., Chen, F., Wen, X.-Y.: Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions and rogue wave solutions. Adv. Differ. Equ. 2016, 67 (2016)
Ankiewicz, A., Soto-Crespo, J.M., Akhmediev, N.: Rogue waves and rational solutions of the Hirota equation. Phys. Rev. E 81, 046602 (2010)
Nikolić, S.N., Aleksić, N.B., Ashour, O.A., Belić, M.R., Chin, S.A.: Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. Nonlinear Dyn. 89, 1637–1649 (2017)
Chowdury, A., Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Breather solutions of the integrable nonlinear Schrödinger equation and their interactions. Phys. Rev. E 91, 022919 (2015)
Yang, Y., Yan, Z., Malomed, B.A.: Rogue waves, rational solitons, and modulational instability in an integrable fifth-order nonlinear Schrödinger equation. Chaos 25, 103112 (2015)
Nikolić, S.N., N.B., Aleksić, Ashour, O.A., Belić, M.R., Chin, S.A.: Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds. Nonlinear Dyn. 95, 2855–2865 (2019)
Nikolić, S.N., Ashour, O.A., Aleksić, N.B., Zhang, Y., Belić, M.R., Chin, S.A.: Talbot carpets by rogue waves of extended nonlinear Schrödinger equations. Nonlinear Dyn. 97, 1215 (2019)
Yin, Y.H., Lü, X., Ma, W.X.: Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dyn. 108, 4181–4194 (2022)
Liu, B., Zhang, X.E., Wang, B., Lü, X.: Rogue waves based on the coupled nonlinear Schrödinger option pricing model with external potential. Modern Phys. Lett. B 36, 2250057 (2022)
Lü, X., Chen, S.J.: Interaction solutions to nonlinear partial differential equations via Hirota bilinear forms: one-lump-multi-stripe and one-lump-multi-soliton types. Nonlinear Dyn. 103, 947–977 (2021)
Zhao, Y.W., Xia, J.W., Lü, X.: The variable separation solution, fractal and chaos in an extended coupled (2+1)-dimensional Burgers system. Nonlinear Dyn. 108, 4195–4205 (2022)
Yin, M.Z., Zhu, Q.W., Lü, X.: Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model. Nonlinear Dyn. 106, 1347–1358 (2021)
Lü, X., Hui, H.W., Liu, F.F., Bai, Y.L.: Stability and optimal control strategies for a novel epidemic model of COVID-19. Nonlinear Dyn. 106, 1491–1507 (2021)
Chaohao, G. (ed.): Soliton Theory and Its Applications. Springer-Verlag, Berlin, Heidelberg (1995)
Gardner, C.S., Greene, J.M., Kruskal, M.D., Miura, R.M.: Method for Solving the Korteweg-deVries Equation. Phys. Rev. Lett. 19, 1095 (1967)
Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. J. Exp. Theor. Phys. 34, 62 (1972)
Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249–315 (1974)
Liu, M.Z., Cao, X.Q., Zhu, X.Q., Liu, B.N., Peng, K.C.: Variational Principles and Solitary Wave Solutions of Generalized Nonlinear Schrödinger Equation in the Ocean. J. Appl. Comput. Mech. 7(3), 1639–1648 (2021)
Matveev, V.B., Salle, M.A.: Darboux Transformations and Solitons. Springer, Berlin, Heidelberg (1991)
Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Circular rogue wave clusters. Phys. Rev. E 84, 056611 (2011)
He, J.H.: Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos Solitons Fractals 19, 847–851 (2004)
Akhmediev, N.N., Korneev, V.I.: Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 69, 1089 (1986)
Akhmediev, N., Eleonskii, V., Kulagin, N.: Exact first-order solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 72, 809 (1987)
Kibler, B., Fatome, J., Finot, C., Millot, G., Genty, G., Wetzel, B., Akhmediev, N., Dias, F., Dudley, J.M.: Observation of Kuznetsov-Ma soliton dynamics in optical fibre. Sci. Rep. 2, 463 (2012)
Xiong, H., Gan, J., Wu, Y.: Kuznetsov-Ma Soliton Dynamics Based on the Mechanical Effect of Light. Phys. Rev. Lett. 119, 153901 (2017)
Dai, C.Q., Wang, Y.Y.: Controllable combined Peregrine soliton and Kuznetsov-Ma soliton in PTPT-symmetric nonlinear couplers with gain and loss. Nonlinear Dyn. 80, 715–721 (2015)
Kibler, B., Fatome, J., Finot, C., Millot, G., Dias, F., Genty, G., Akhmediev, N., Dudley, J.M.: The Peregrine soliton in nonlinear fibre optics. Nature Phys. 6, 790–795 (2010)
Shrira, V.I., Geogjaev, V.V.: What makes the Peregrine soliton so special as a prototype of freak waves? J. Eng. Math. 67, 11 (2010)
Dudley, J.M., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nature Phot. 8, 755 (2014)
Peregrine, D.H.: Water waves, nonlinear Schrödinger equations and their solutions. J. Austral. Math. Soc. B 25, 16 (1983)
Solli, D.R., Ropers, C., Jalali, B.: Active control of rogue waves for stimulated supercontinuum generation. Phys. Rev. Lett. 101, 233902 (2008)
Dudley, J.M., Genty, G., Eggleton, B.J.: Harnessing and control of optical rogue waves in supercontinuum generation. Opt. Express 16, 3644 (2008)
Ganshin, A.N., Efimov, V.B., Kolmakov, G.V., Mezhov-Deglin, L.P., McClintock, P.V.E.: Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium. Phys. Rev. Lett. 101, 065303 (2008)
Bludov, Y.V., Konotop, V.V., Akhmediev, N.: Matter rogue waves. Phys. Rev. A 80, 033610 (2009)
Li, Z.-Y., Li, F.-F., Li, H.-J.: Exciting rogue waves, breathers, and solitons in coherent atomic media. Commun. Theor. Phys. 72, 075003 (2020)
Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005)
Nikolić, S.N., Radonjić, M., Krmpot, A.J., Lučić, N.M., Zlatković, B.V., Jelenković, B.M.: Effects of a laser beam profile on Zeeman electromagnetically induced transparency in the Rb buffer gas cell. J. Phys. B: At. Mol. Opt. Phys. 46, 075501 (2013)
Krmpot, A.J., Ćuk, S.M., Nikolić, S.N., Radonjić, M., Slavov, D.G., Jelenković, B.M.: Dark Hanle resonances from selected segments of the Gaussian laser beam cross-section. Opt. Express 17, 22491–22498 (2009)
Nikolić, S.N., Radonjić, M., Lučić, N.M., Krmpot, A.J., Jelenković, B.M.: Transient development of Zeeman electromagnetically induced transparency during propagation of Raman-Ramsey pulses through Rb buffer gas cell. J. Phys. B: At. Mol. Opt. Phys. 48, 045501 (2015)
Akhmediev, N., Soto-Crespo, J.M., Ankiewicz, A.: How to excite a rogue wave. Phys. Rev. A 80, 043818 (2009)
Chin, S.A., Ashour, O.A., Belić, M.R.: Anatomy of the Akhmediev breather: cascading instability, first formation time, and Fermi-Pasta-Ulam recurrence. Phys. Rev. E 92, 063202 (2015)
Belić, M.R., Nikolić, S.N., Ashour, O.A., Aleksić, N.B.: On different aspects of the optical rogue waves nature. Nonlinear Dyn. 108, 1655–1670 (2022)
Nikolić, S.N., Alwashahi, S., Ashour, O.A., Chin, S.A., Aleksić, N.B., Belić, M.R.: Multi-elliptic rogue wave clusters of the nonlinear Schrödinger equation on different backgrounds. Nonlinear Dyn. 108, 479–490 (2022)
Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Triangular rogue wave cascades. Phys. Rev. E 86, 056602 (2012)
Dubard, P., Gaillard, P., Klein, C., Matveev, V.B.: On multi-rogue wave solutions of the NLS equation and positon solutions of the KdV equation. Eur. Phys. J. Special Topics 185, 247 (2010)
Ohta, Y., Yang, J.: General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation. Proc. R. Soc. A 468, 1716 (2012)
Gaillard, P.: Degenerate determinant representation of solutions of the nonlinear Schrödinger equation, higher order Peregrine breathers and multi-rogue waves. J. Math. Phys. 54, 013504 (2013)
Ankiewicz, A., Akhmediev, N.: Multi-rogue waves and triangular numbers. Romanian Rep. Phys. 69, 104 (2017)
He, J.S., Zhang, H.R., Wang, L.H., Porsezian, K., Fokas, A.S.: Generating mechanism for higher-order rogue waves. Phys. Rev. E 87, 052914 (2013)
Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Classifying the hierarchy of nonlinear-Schödinger-equation rogue-wave solutions. Phys. Rev. E 88, 013207 (2013)
Akhmediev, N.: Waves that appear from nowhere: complex rogue wave structures and their elementary particles. Front. Phys. 8, 612318 (2021)
Chin, S.A., Ashour, O.A., Nikolić, N.N., Belić, M.R.: Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation. Phys. Lett. A 380, 3625 (2016)
Chin, S.A., Ashour, O.A., Nikolić, S.N., Belić, M.R.: Peak-height formula for higher-order breathers of the nonlinear Schrödinger equation on nonuniform backgrounds. Phys. Rev. E 95, 012211 (2017)