2013/10/31 by Xi-Zhong Liu, Jun Yu, Liu, Xi-zhong +3
Chemistry · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1310.8512
openalex publication_date 2013/10/31 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
The Backlund transformation related symmetry is nonlocal, which is hardly to apply in constructing solutions for nonlinear equations. In this paper, we first localize nonlocal residual symmetry to Lie point symmetry by introducing multiple new variables and obtain new Baaklund transformation. Then, by solving out the general form of localized the residual symmetry, we reduce the enlarged system by classical symmetry approach and obtain the corresponding reduction solutions as well as related reduction equations. The localization procedure provides a new way to investigate interaction solutions between different waves.