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Hong Li, Lilin Ma, Kanmin Wang. SOLITARY WAVE AND CHAOTIC BEHAVIOR OF TRAVELING WAVE SOLUTIONS FOR THE COUPLED SCHRÖDINGER-KDV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1073-1080. doi: 10.11948/2016070

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Hong Li, Lilin Ma, Kanmin Wang. SOLITARY WAVE AND CHAOTIC BEHAVIOR OF TRAVELING WAVE SOLUTIONS FOR THE COUPLED SCHRÖDINGER-KDV EQUATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1073-1080. doi: 10.11948/2016070

SOLITARY WAVE AND CHAOTIC BEHAVIOR OF TRAVELING WAVE SOLUTIONS FOR THE COUPLED SCHRÖDINGER-KDV EQUATIONS

1 Department of Mathematics, Jiujiang University, Jiujiang 332005, China;
2 Information Technology Center, Jiujiang University, Jiujiang 332005, China

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Abstract

Abstract

This paper deals with the coupled Schrödinger-KdV equations by making use of the method of dynamical systems. We obtain some exact explicit parametric representations of the solitary wave and periodic wave solutions in the given parameter regions, and study chaotic behavior of travelling wave solutions.
- Coupled Schrö /
- dinger-KdV equations /
- travelling wave solution /
- chaotic behavior of travelling wave /
- solitary wave solution
MSC: 34C60;35Q51;35C05;35C07

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References

[1]	V. I. Arnold, Instability of dynamical systems with several degrees of freedom, Sov. Math. Dokl., 5(1964), 581-585. Google Scholar
[2]	A. Y. Chen, S. Q. Wen, S. Q. Tang et al., Effects of quadratic singular curves in integrable equations, Stud. Appl. Math., 134(2015)(1), 24-61. Google Scholar
[3]	J. Guckenheimer and P. J. Holmes, Dynamical Systems and Bifurcation of Vector Fields, Springer-Verlag, New York, 1983. Google Scholar
[4]	M. A. Han and D. M. Zhu, Bifurcation Theory of Differential Equation, China Coal Industry Publishing House, Beijing, 1994. Google Scholar
[5]	P. J. Holmes and J. E. Marsdan, Horseshoes in perturbation of Hamiltonian with two degrees of freedom, Commun. Math. Phys., 82(1982)(4), 523-544. Google Scholar
[6]	P. J. Holmes and J. E. Marsden, A partial differential equation with infinitely many periodic orbits:chaotic oscillations of a forced beam, Arch. Rat. Mech. Anal., 76(1981)(2), 135-165. Google Scholar
[7]	J. B. Li, Note on exact travelling wave solutions for a long wave-short wave model, J. Appl. Anal and Computation, 5(2015)(1), 138-140. Google Scholar
[8]	J. B. Li and H. H. Dai, On the Study of Singular Nonlinear Travelling Wave Equations:Dynamical System Approach, Science Press, Beijing, 2007. Google Scholar
[9]	H. Z. Liu and Y. X. Geng, Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid, J. Differ. Equations, 254(2013)(5), 2289-2303. Google Scholar
[10]	V. K. Melnikov, On the stability of the centre for time-periodic perturbations, Trans. Mosc. Math. Soc., 12(1963), 1-57. Google Scholar
[11]	S. Q. Tang, L. J. Qiao and H. L. Fu, Peakon soliton solutions of k(2,-2,4) equation, J. Appl. Anal and Computation, 3(2013)(4), 399-403. Google Scholar
[12]	S. Wiggins, Global Bifurcations and Chaos, Springer-Verlag, New York, 1988. Google Scholar