Exponentially localized solutions of Mel'nikov equation
نویسندگان
چکیده
منابع مشابه
Exponentially Localized Solutions of Mel’nikov Equation
The Mel’nikov equation is a (2+1) dimensional nonlinear evolution equation admitting boomeron type solutions. In this paper, after showing that it satisfies the Painlevé property, we obtain exponentially localized dromion type solutions from the bilinearized version which have not been reported so far. We also obtain more general dromion type solutions with spatially varying amplitude as well a...
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Exponentially localized solutions of the Klein-Gordon equation for two and three space variables are presented. The solutions depend on four free parameters. For some relations between the parameters, the solutions describe wave packets filled with oscillations whose amplitudes decrease in the Gaussian way with distance from a point running with group velocity along a straight line. The solutio...
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A general functional separation solution, containing two arbitrary functions, is first obtained for the Melnikov equation by means of the singular manifold method. Some novel localized coherent structures are given by appropriately choosing these arbitrary functions, whose interaction properties are numerically studied. The creation and annihilation phenomenon of dromion structure is reported. ...
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Exact periodic wave solutions in terms of the Jacobi elliptic functions are obtained to the Melnikov equation by means of the extended mapping method with symbolic computation. The stability of these periodic waves is numerically studied. The results show that the linearly combined waves of cn− and dn− functions can propagate stably. For the blow up solutions, the linearly combined periodic sol...
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ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2004
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2004.02.046