Abstract
The existing symmetry approach to exactly solvable time-evolution equations in one spatial dimension is extended to the case that the equation depends explicitly on the time and space coordinates. In this context (commuting) symmetries, constants of motion (in involution), strong and hereditary symmetries (squared-eigenfunction operators), and Hamiltonian structures are discussed. The cylindrical Korteweg–de Vries equation is used as an illustrative example.
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