Bi-Variationality, Symmetries and Approximate Solutions

By a bi-variational system we mean any system of equations generated by two different Hamiltonian actions. A connection between their variational symmetries is established. The effective use of the nonclassical Hamiltonian actions for the construction of approximate solutions with high accuracy for the given dissipative problem is demonstrated. We also investigated potentiality of the given operator equation with the second time derivative, constructed the corresponding functional and found necessary and sufficient conditions for an operator S to be a generator of symmetry of the constructed functional. Theoretical results are illustrated by some examples.