Exponentially Localized Solutions of Mel'nikov Equation

Abstract

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 as induced multi-dromion solutions.

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

References in corpus (1)

• Explode-decay dromions in the non-isospectral Davey-Stewartson I (DSI) equation

Cited by in corpus (3)

• Self-Consistent Sources for Integrable Equations via Deformations of Binary Darboux Transformations
• General $N$-Dark Soliton Solutions of the Multi-Component Mel'nikov System
• Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation