期刊
APPLIED MATHEMATICAL MODELLING
卷 40, 期 5-6, 页码 3475-3482出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.09.006
关键词
Generalizing Riccati equation mapping method; Improved projective Riccati equation method; Localized coherent structure; Variable separation solution
资金
- National Natural Science Foundation of China [11404289, 11375007]
- Scientific Research and Developed Fund of Zhejiang A F University [2014FR020]
- Foundation of New Century 151 Talent Engineering of Zhejiang Province in China
- Youth Top-notch Talent Development and Training Program of Zhejiang AF University
Caution is advised regarding so-called new variable separation solutions obtained by the generalizing Riccati equation mapping method and the improved projective Riccati equation method because many seemingly independent variable separation solutions actually depend on each other. To illustrate this point, we employ the (2+1)-dimensional Bogoyavlenskii-Schiff model as an example and we derive 10 different variable separation solutions. Based on a detailed investigation, we show that many of the so-called new solutions are equivalent to each other. Thus, when we discuss localized structures based on variable separation solution, we should consider all of the field components to avoid the appearance of false unphysical related structures, where seemingly abundant structures are obtained for a special component, while unphysical (non-localized) or even divergent structures may appear for other corresponding components of the same equation. (C) 2015 Elsevier Inc. All rights reserved.
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