Be careful with the equivalence of different ansätz of improved tanh-function method for nonlinear models. (October 2015)

• Record Type: Journal Article
• Authors: Lou, Mu-Ren; Zhang, Yu-Peng; Kong, Liang-Qian; Dai, Chao-Qing
• Is Part Of: Applied mathematics letters. Volume 48(2015:Oct.)
• Page Start: 23
• Page End: 29
• Publication Date: 2015-10
• Subjects: Improved tanh-function method -- Positive-power ansatz -- Positive and negative power-symmetric ansatz -- Radical sign combined ansatz -- Breaking soliton model; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.03.009
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Exact solutions of nonlinear models might explain real physical, engineering and biophysical problems, including blood pressure waves, α -helical protein, matter wave and hardening spring effect, and so on. We re-study the breaking soliton model and obtain eleven kinds of variable separation solution by means of the improved tanh-function method with three different ansätz, that is, positive-power ansatz, radical sign combined ansatz, and positive and negative power-symmetric ansatz. By careful analysis of these exact solutions, we find that these seemly independent variable separation solutions actually depend on each other. Therefore, different ansätz of improved tanh-function method are equivalent.