Nonlocal Symmetry and Bäcklund Transformation of a Negative-Order Korteweg–de Vries Equation - Jinxi Fei; Weiping Cao; Zhengyi Ma (Complexity, 2019)
The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By using Lie’s first theorem, we obtain the finite transformation for the localized residual symmetry. Furthermore, we localize the linear superposition of multiple residual symmetries and construct n-th Bäcklund transformation for this nKdV equation in the form of the determinants.