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非局部两分量耦合复可积无色散方程的孤子解
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Abstract:
本文提出了一种非局部两分量耦合复可积无色散方程。利用达布变换方法得到了零种子解和非零种子解两种情况下，非局部两分量耦合复可积无色散方程的孤子解。
In this paper, a nonlocal two-component complex coupled integrable dispersionless equation is proposed. The soliton solutions of nonlocal two-component coupled complex integrable dispersion-less equations are obtained by using darboux transformation method under two cases of zero seed solution and non-zero seed solution.
| [1] | Konno, K. and Oono, H. (1994) New Coupled Integrable Dispersionless Equations. Journal of the Physical Society of Japan, 63, 377-378. https://doi.org/10.1143/JPSJ.63.377 |
| [2] | Alagesan, T. and Porsezian, K. (1996) Painleve Analysis and the Integrability Properties of Coupled Integrable Dispersionless Equations. Chaos, Solitons & Fractals, 7, 1209-1212. https://doi.org/10.1016/0960-0779(95)00108-5 |
| [3] | Kakuhata, H. and Konno, K. (1999) Loop Soliton Solutions of String Interacting with External Field. Journal of the Physical Society of Japan, 68, 757-762. https://doi.org/10.1143/JPSJ.68.757 |
| [4] | Hirota, R. and Tsujimoto, S. (1994) Note on New Coupled Integrable Dispersionless Equations. Journal of the Physical Society of Japan, 63, 3533. https://doi.org/10.1143/JPSJ.63.3533 |
| [5] | Konno, K. and Oono, H. (1994) Reply to Note on New Coupled Inte-grable Dispersionless Equations. Journal of the Physical Society of Japan, 63, 3534. https://doi.org/10.1143/JPSJ.63.3534 |
| [6] | Kotlyarov, V.P. (1994) On Equations Gauge Equivalent to the Si-ne-Gordon and Pohlmeyer-Lund-Regge Equations. Journal of the Physical Society of Japan, 63, 3535-3537. https://doi.org/10.1143/JPSJ.63.3535 |
| [7] | Konno, K. (1995) Integrable Coupled Dispersionless Equations. Appli-cable Analysis, 57, 209-220.
https://doi.org/10.1080/00036819508840347 |
| [8] | Kakuhata, H. and Konno, K. (1996) A Generalization of Cou-pled Integrable Dispersionless System. Journal of the Physical Society of Japan, 65, 340-341. https://doi.org/10.1143/JPSJ.65.340 |
| [9] | Peregrine, D.H. (1983) Water Waves, Nonlinear Schr？dinger Equations and Their Solutions. The ANZIAM Journal, 25, 16-43. https://doi.org/10.1017/S0334270000003891 |
| [10] | Akhmediev, N., Ankiewicz, A. and Soto-Crespo, J.M. (2009) Rogue Waves and Rational Solutions of the Nonlinear Schr？dinger Equation. Physical Review E, 80, Article ID: 026601. https://doi.org/10.1103/PhysRevE.80.026601 |
| [11] | Akhmediev, N., Ankiewicz, A. and Taki, M. (2009) Waves That Appear from Nowhere and Disappear without a Trace. Physics Letters A, 373, 675-678. https://doi.org/10.1016/j.physleta.2008.12.036 |
| [12] | Ankiewicz, A., Kedziora, D.J. and Akhmediev, N. (2011) Rogue Wave Triplets. Physics Letters A, 375, 2782-2785.
https://doi.org/10.1016/j.physleta.2011.05.047 |
| [13] | Yan, Z.Y. (2010) Financial Rogue Waves. Communications in Theoretical Physics, 54, 947-949.
https://doi.org/10.1088/0253-6102/54/5/31 |
| [14] | Yoshimasa, M. (2007) Multiloop Soliton and Multibreather Solu-tions of the Short Pulse Model Equation. Journal of the Physical Society of Japan, 76, Article ID: 084003. https://doi.org/10.1143/JPSJ.76.084003 |
| [15] | Feng, B.F. (2015) Complex Short Pulse and Coupled Complex Short Pulse Equations. Physica D: Nonlinear Phenomena, 297, 62-75. https://doi.org/10.1016/j.physd.2014.12.002 |
| [16] | Shen, S.F., Feng, B.F. and Ohta, Y. (2016) From the Real and Complex Coupled Dispersionless Equations to the Real and Complexshort Pulse Equations. Studies in Applied Mathe-matics, 136, 64-88. https://doi.org/10.1111/sapm.12092 |
| [17] | Ling, L., Feng, B.F. and Zhu, Z.N. (2016) Mul-ti-Soliton, Multi-Breather and Higher Order Rogue Wave Solutions to the Complex Short Pulse Equation. Physica D: Nonlinear Phenomena, 327, 62-75.
https://doi.org/10.1016/j.physd.2016.03.012 |
| [18] | Feng, B.F., Ling, L. and Zhu, Z.N. (2016) Defocusing Complex Short-Pulse Equation and Its Multi-Dark-Soliton Solution. Physical Review E, 93, Article ID: 052227. https://doi.org/10.1103/PhysRevE.93.052227 |
| [19] | Ji, J.L., Huang, Z.L. and Zhu, Z.N. (2017) Reverse Space and Time Nonlocal Coupled Dispersionless Equation and Its Solutions. Annals of Mathematical Sciences and Applications, 2, 409-429.
https://doi.org/10.4310/AMSA.2017.v2.n2.a8 |
