Exponentially Localized Solutions of Mel'nikov Equation

Details Exponentially Localized Solutions of Mel'nikov Equation Exponentially Localized Solutions of Mel'nikov Equation

2004-03-22

arxiv.org/abs/nlin/0403044v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 2 figures, to appear in Chaos, Solitons and Fractals

Scientific paper

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 Painlev\'{e} 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 as induced multi-dromion solutions.

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