理论数学  >> Vol. 1 No. 2 (July 2011)

非等谱mKP方程的孤子共振解
Soliton Resonance of the NI-mKP Equation

DOI: 10.12677/pm.2011.12021, PDF, HTML, 下载: 2,730  浏览: 9,479 

作者: 吴妙仙, 颜姣姣

关键词: 共振孤子方程Hirota双线性方法非等谱mKP方程T
Resonance; Soliton Equation; Hirota Bilinear Method; Nonisospectral mKP Equatin

摘要: 共振是孤子相互作用的一种现象,本文利用渐进分析法研究了非等谱修正Kadomtsev-Petviashvili(mKP)方程的共振解。首先使用Hirota双线性方法得出其2孤子和3孤子解,然后通过详细的图像分析、比较,研究了2,3孤子的各种共振现象。
Abstract: Resonance is one of soliton interaction phenomenon, in this peper the soliton resonance of the NI-modified Kadomtsev-Petviashvili (mKP) equation will be studied by asymptotic analysis. At first, its 2-and 3-soliton solution will be presented using Hirota bilinear method, then we will further study the reso-nance property of 2 and 3 soliton solutions through the detail image analysis and comparison.

文章引用: 吴妙仙, 颜姣姣. 非等谱mKP方程的孤子共振解[J]. 理论数学, 2011, 1(2): 99-106. http://dx.doi.org/10.12677/pm.2011.12021

参考文献

[1] R. Hirota, J. Satsuma. Nonlinear evolution equations generated from the Bäcklund transformation for the Boussinesq equation. Progress of Theoretical Physics, 1977, 57(3): 797-807.
[2] R. Hirota. Exact solution to the Korteweg-de Vries equation for multiple collisions of solitons. Physical Review Letters, 1971, 27(18): 1192-1194.
[3] X. B. Hu, P. A. Clarkson. Rational solutions of a differential- difference KdV equation, the toda equation and the discrete KdV equation. Journal of Physics A: Mathematical and Theoretical, 1995, 28(17): 5009-5016.
[4] 张大军, 邓淑芳. 孤子解的Wronskian表示[J]. 上海大学学报:自然科学版, 2002, 8(3): 232-242.
[5] Y. D. Zhang, Y. Chen. A new representation of N-solition solution ang limiting solution for the fitth order KdV equation. Chaos, Solitons and Fractals, 2005, 23(3): 1055-1061.
[6] N. C. Freeman, J. J. C. Nimmo. Soliton solutions of the Korteweg-de Vries and Kadomtsev Petmiashvili equations: The Wronskian technique. Physics Letters, 1983, 95A(1): 1-3.
[7] 陈登远. Bäcklund变换与n孤子解[J]. 数学研究与评论, 2005, 25(3): 479-488.
[8] 陈登远. 孤子引论[M]. 北京: 科学出版社, 2006: 101-122.
[9] S. L. Lou, L. L. Chen, Formally variable separation approach for nonintegrable models. Journal of Mathematical Physics, 1990, 40(5): 6491-6500.
[10] Z. S. Lu, H. Q. Zhang. On a further extended tanh method. Physics Letter A, 2003, 307(5-6): 269-273.
[11] 范恩贵. 齐次平衡法, Weiss-Tabor-Carnevale 及 Clarkson- Kruskal约化之间的联系[J]. 物理学报, 1998, 47(8): 1409- 1412.
[12] J. W. Milesm. Resonantly interacting solitary waves. The Journal of Fluid Mechanics, 1977, 79(1): 171-179.
[13] F. Lambert, M. Musette. Tow-soliton resonances for KdV- like solitary waves. Journal of the Physical Society of Japan, 1987, 57(6): 2207-2208.
[14] K. Ohkuma, M. Wadati. The Kadomtsev-Petviashvili equation: the trace method and the soliton resonances. Journal of the Physical Society of Japan, 1983, 52(3): 749-760.
[15] E. Medina. An N soliton resonance solution for the KP equation: interaction with change of form and velocity. Letters in Mathematical Physics, 2002, 62(2): 91-99.
[16] S. Isojima, R. Willox, J. Satsuma. On various solutions of the coupled KP equation. Journal of Physics A, 2002, 35(32): 6893- 6909.
[17] O. K. Pashaev, M. L. Y. Francisco. Degenerate four-virtual- soliton resonance for the KP-II. Theoretical and Mathematical Physics, 2005, 144(1): 1022-1029.
[18] J. H. Lee, R. Willox, O. K. Pashaev. Soliton resonances for the MKP-II. Theoretical and Mathematical Physics, 2005, 144(1): 995-1003.
[19] H. H. Hao, D. J. Zhang. Resonance of line solitons in a non-isospectral Kadomtsev-Petviashvili equation. Journal of the Physical Society of Japan, 2008, 77(1-4): Article ID 045001-2.
[20] S. F. Deng. The multisoliton solutions for the nonisospectral mKP equation. Physics Letters A, 2007, 362(2-3):198-204.
[21] Y. Zhang, Y. N. Lv. On the nonisospectral modified Kadomtsev-Peviashvili equation. Journal of Mathematical Analysis and Applications, 2008, 342(1): 534-541.