Trilinearization and localized coherent structures and periodic solutions for the (2 + 1) dimensional K-dV and NNV equations |
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| Authors: | C. Senthil Kumar R. Radha M. Lakshmanan |
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| Affiliation: | 1. School of Sciences, Zhejiang A&F University, Lin’an, Zhejiang 311300, PR China;2. Zhejiang Provincial Key Laboratory of Chemical Utilization of Forestry Biomass, Zhejiang A&F University, Lin’an, Zhejiang 31130, PR China;3. School of Electronics Information, Zhejiang University of Media and Communications, Hangzhou 310018, PR China;1. Centre for Nonlinear Science, PG and Research Department of Physics, Government College for Women (Autonomous), Kumbakonam 612001, India;2. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel |
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| Abstract: | In this paper, using a novel approach involving the truncated Laurent expansion in the Painlevé 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. |
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