Geodesic
Bi-variationality, symmetries and approximate solutions
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 596-608

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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 the high accuracy for the given dissipative problem is demonstrated. We also investigate the potentiality of the given operator equation with the second-order time derivative, construct the corresponding functional and find necessary and sufficient conditions for the operator $S$ to be a generator of symmetry of the constructed functional. Theoretical results are illustrated by some examples. 
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     title = {Bi-variationality, symmetries and approximate solutions},
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     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a12/}
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V. M. Filippov; V. M. Savchin; S. A. Budochkina. Bi-variationality, symmetries and approximate solutions. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 596-608. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a12/