Eur. Phys. J. Plus (2015) 130: 242
https://doi.org/10.1140/epjp/i2015-15242-x

Regular Article

Discussions on equivalent solutions and localized structures via the mapping method based on Riccati equation

School of Sciences, Zhejiang Agriculture and Forestry University, 311300, Lin’an, Zhejiang, P.R. China

^* e-mail: dcq424@126.com

Received: 1 September 2015
Accepted: 2 November 2015
Published online: 4 December 2015

Abstract

Although the mapping method based on Riccati equation was proposed to obtain variable separation solutions many years ago, two important problems have not been studied: i) the equivalence of variable separation solutions by means of the mapping method based on Riccati equation with the radical sign combined ansatz; and ii) lack of physical meanings for some localized structures constructed by variable separation solutions. In this paper, we re-study the (2+1)-dimensional Boiti-Leon-Pempinelli equation via the mapping method based on Riccati equation and prove that nine types of variable separation solutions are actually equivalent to each other. Moreover, we also re-study localized structures constructed by variable separation solutions. Results indicate that some localized structures reported in the literature are lacking real values due to the appearance of the divergent and un-physical phenomenon for the initial field. Therefore, we must be careful with the initial field to avoid the appearance of some un-physical or even divergent structures in it when we construct localized structures for the potential field.