Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-01-21
Nonlinear Sciences
Exactly Solvable and Integrable Systems
19 pages, 7 figures. to appear in Chaos, Solitons and Fractals
Scientific paper
In this paper, using a novel approach involving the truncated Laurent expansion in the Painlev\'e analysis of the (2+1) dimensional K-dV equation, we have trilinearized the evolution equation and obtained rather general classes of solutions in terms of arbitrary functions. The highlight of this method is that it allows us to construct generalized periodic structures corresponding to different manifolds in terms of Jacobian elliptic functions, and the exponentially decaying dromions turn out to be special cases of these solutions. We have also constructed multi-elliptic function solutions and multi-dromions and analysed their interactions. The analysis is also extended to the case of generalized Nizhnik-Novikov-Veselov (NNV) equation, which is also trilinearized and general class of solutions obtained.
Kumar Chaitanya S.
Lakshmanan Meenakshi
Radha R.
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