1 Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;
2 Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere and Faculty of Science, Ningbo University, Ningbo 315211, China
For a given truncated Painlevé expansion of an arbitrary nonlinear Painlevé integrable system, the residue with respect to the singularity manifold is known as a nonlocal symmetry, called the residual symmetry, which is proved to be localized to Lie point symmetries for suitable prolonged systems. Taking the Korteweg-de Vries equation as an example, the n-th binary Darboux-Bäcklund transformation is re-obtained by the Lie point symmetry approach accompanied by the localization of the n-fold residual symmetries.
Project supported by the National Natural Science Foundation of China (Grant Nos.11675055,11175092,and 11205092),the Program from Shanghai Knowledge Service Platform for Trustworthy Internet of Things (Grant No.ZF1213),and K C Wong Magna Fund in Ningbo University.
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