Symmetries, conservation laws and Hamiltonian structures of the non-isospectral and variable coefficient KdV and MKdV equations

Abstract

An infinite number of form-invariant symmetries is obtained and a one-to-one correspondence between symmetries and conservation laws is established for the non-isospectral and variable coefficient generalizations of both the KdV and the MKdV equations. Two families of symmetries and their Lie algebraic structures are constructed. Some interesting facts about their Hamiltonian structures are presented.