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	Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrodinger equations
	Zhu, Yi ; Yang, Jianke
	2010-05-06 ; 2010-05-06
关键词	KINK-ANTIKINK INTERACTIONS SINE-GORDON EQUATION IMPURITY INTERACTIONS VECTOR SOLITONS BOUND-STATES COLLISIONS RESONANCE MODEL SYSTEMS FIBERS Physics, Fluids & Plasmas Physics, Mathematical
中文摘要	Weak interactions of solitary waves in the generalized nonlinear Schrodinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is nonzero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schrodinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.
语种	英语 ; 英语
出版者	AMERICAN PHYSICAL SOC ; COLLEGE PK ; ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14002]
专题	清华大学
推荐引用方式 GB/T 7714	Zhu, Yi,Yang, Jianke. Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrodinger equations[J],2010, 2010.
APA	Zhu, Yi,&Yang, Jianke.(2010).Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrodinger equations..
MLA	Zhu, Yi,et al."Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrodinger equations".(2010).

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