Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

Abstract:

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

• Periodical: Applied Mechanics and Materials (Volume 340)
• Pages: 755-759
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.340.755
• Online since: July 2013
• Authors: Song Hua Ma
• Keywords: (G'/G)-Expansion Approach, Chaotic Patterns, Modified Dispersive Water-Wave System - Exact Solutions

References

[1] Qian SP, Tian LX (2007) Lie symmetry analysis and reduction of a new integral coupled KdV system. Chin. Phys. B 16(2): 303-307.

[2] Yang XY, Tang JS (2007) New travelling wave solutions for combined KdV. mKdV equation and (2+1)-dimensional Broer-Kaup-Kupershmidt system. Chin. Phys. B 16(2): 310-317.

DOI: 10.1088/1009-1963/16/2/007

[3] Wang YH, Chen Y (2011) Binary bell polynomials bilinear approach to exact periodic wave solutions of (2+1)-dimensional nonlinear evolution equation. Common Theory Phys 56(4): 672-678.

DOI: 10.1088/0253-6102/56/4/14

[4] Lai G, Sheng WC (2010) Simple waves for two-dimensional compressible pseudo-steady Euler system. Appl. Math. Mech 31(7): 827-838.

DOI: 10.1007/s10483-010-1317-7

[5] Tang YN, Ma WX, Xu W (2012) Grampian and Pfaffian solutions as well as Pfaffanization for a (3+1)-dimensional generalized shallow water equation. Chin. Phys. B 21(7): 207-212(1-7).

[6] Huang WH, Zhang JF, Sheng ZM (2002) Coherent solution structures of the (2+1)-dimensional long-wave short-wave resonance interaction equation. Chin. Phys. B 11(11): 1101-1105.

DOI: 10.1088/1009-1963/11/11/302

[7] Zhang JF, Guo GP, Wu FM (2002) new multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations. Chin. Phys. B 11(6): 533-536.

DOI: 10.1088/1009-1963/11/6/303

[8] Ma ZY, Zheng CL (2006) Two classes of fractal structures for the (2+1)-dimensional dispersive long wave system. Chin. Phys. B 15(01): 0045-0052.

[9] Zhu JM, Ma ZY (2005) an extended Jacobian elliptic function method for the discrete mKdV lattice. Chin. Phys. B 14(01): 0017-0020.

[10] Fang JP, Zheng CLZhu JM, Ren QB (2005) new family of excite solutions and chaotic solitons of generalized Breor-Kaup system in (2+1)-dimensions via an extended mapping approach. Common Theory Phys 44(02): 203-208.

DOI: 10.1088/6102/44/2/203

[11] Fang JP, Zhen CL, Liu Q (2005) No propagating solution in (2+1)-dimensional dispersive long-water system. Commune Theory Phys 43(02): 245-250.

[12] Ma SH, Fang JP, Zheng CL (2008) Complex wave excitations and chaotic patterns for a generalized (2+1)-dimensional korteweg de-vries system. Chin. Phys. B 17(8): 2767-2773.

DOI: 10.1088/1674-1056/17/8/004

[13] Ma SH, Wu XH, Fang JP, Zheng CL (2009) New exact solutions for the (3+1)-dimensional Jimbo-Miwa system. Chaos Solutions and Fractals 40(3): 1352-1355.

DOI: 10.1016/j.chaos.2007.09.012

[14] Ma SH, Fang JP, Zheng CL (2009) New exact solutions of the (2+1)-dimensional breaking soliton system via an extended mapping method. Chaos Solutions and Fractals 40(1): 210-214.

DOI: 10.1016/j.chaos.2007.07.043

[15] Ma SH, Fang JP, Ren QB (2010) Instantaneous embed solution and instantaneous taper-like soliton for the (3+1)-dimensional Burgers system. Acta Phys. Sin 59(7): 4420-4425.

DOI: 10.7498/aps.59.4420