Notes on the equivalence of different variable separation approaches for nonlinear evolution equations

作者：Dai Chao Qing^*; Wang Yue Yue

来源：Communications in Nonlinear Science & Numerical Simulation, 2014, 19(1): 19-28.

DOI：10.1016/j.cnsns.2013.05.027

• Variable separation solutions
• Equivalence of different methods
• (2+1)-Dimensional modified Broer-Kaup system
• Localized structures

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.

• 出版日期2014-1
• 单位浙江农林大学