Nonlocal symmetries and recursion operators: Partial differential and differential-difference equations |
| |
Authors: | R Sahadevan S Khousalya L Nalini Devi |
| |
Institution: | Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600 005, Tamil Nadu, India |
| |
Abstract: | A systematic method to derive the nonlocal symmetries for partial differential and differential-difference equations with two independent variables is presented and shown that the Korteweg-de Vries (KdV) and Burger's equations, Volterra and relativistic Toda (RT) lattice equations admit a sequence of nonlocal symmetries. An algorithm, exploiting the obtained nonlocal symmetries, is proposed to derive recursion operators involving nonlocal variables and illustrated it for the KdV and Burger's equations, Volterra and RT lattice equations and shown that the former three equations admit factorisable recursion operators while the RT lattice equation possesses (2×2) matrix factorisable recursion operator. The existence of nonlocal symmetries and the corresponding recursion operator of partial differential and differential-difference equations does not always determine their mathematical structures, for example, bi-Hamiltonian representation. |
| |
Keywords: | Integrable lattice equations Nonlocal symmetries and recursion operator |
本文献已被 ScienceDirect 等数据库收录! |
|