Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 19, Issue 1, Pages 19-28Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2013.05.027
Keywords
Variable separation solutions; Equivalence of different methods; (2+1)-Dimensional modified Broer-Kaup system; Localized structures
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Funding
- National Natural Science Foundation of China [11005092]
- Zhejiang Provincial Natural Science Foundation of China [Y13F050037]
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The equivalence of multilinear variable separation approach, the extended projective Ricatti equation method and the improved tanh-function method is firstly reported when these three popular methods are used to realize variable separation for nonlinear evolution equations. We take the (2 + 1)-dimensional modified Broer-Kaup system for an example to illustrate this point. All solutions obtained by the extended projective Ricatti equation method and the improved tanh-function method coincide with the one obtained by the multilinear variable separation approach. Moreover, based on one of variable separation solutions, we also find that although abundant localized coherent structures can be constructed for a special component, we must pay our attention to the solution expression of the corresponding other component for the same equation lest many un-physical related structures might be obtained. (c) 2013 Elsevier B.V. All rights reserved.
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