Time-Dependent Recursion Operators and Symmetries
Copyright policy )Time-Dependent Recursion Operators and Symmetries
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion operators do not satisfy the symmetry equations. There have been several attempts to resolve this problem. It is shown that in the case of time dependent evolution equations or time dependent recursion operators, associativity is lost. Due to this fact such recursion operators need modifications. A general formula is given for the missing term of the recursion operators. Apart from the recursion operators a method is introduced to calculate the correct symmetries. For illustrations several examples of scalar and coupled system of equations are considered.
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- Bilkent University Turkey
- Middle East Technical University Turkey
- Bilkent University Turkey
KdV equation, KdV equations (Korteweg-de Vries equations), Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, symmetries, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, recursion operators, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Burgers equation
KdV equation, KdV equations (Korteweg-de Vries equations), Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, symmetries, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, recursion operators, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Burgers equation
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