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Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions

Kindybaliuk A., Prytula M.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 3

85--99

In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.

Construction of algebraic-analytic discrete approximations for linear and nonlinear hyperbolic equations in R2. Pt. 1

Luśtyk M., Prytula M.

Opuscula Mathematica

2007

Vol. 27, no. 1

25-36

An algebraic-analytic method for constructing discrete approximations of linear hyperbolic equations based on a generalized d'Alembert formula of the Lytvyn and Riemann expressions for Cauchy data is proposed. The problem is reduced to some special case of the fixed point problem.