Abstract
There is developed an algorithm to classify integrable nonlinear dynamical systems via Wolfram Mathematica. The hierarchy of conservation laws for the nonlinear dynamical system can be cal-culated by this algorithm. There are demonstrated some modifications of nonlinear Korteweg-de Vries equations integrated by inverse scatering method.
Highlights
It is well known that solving the nonlinear partial equations is quite complicated procedure and the result can’t be ensured
It is application of gradient-holonomic algorithm that makes possible to calculate hierarchy of conservation laws being attached to the algebraic structures
Due to these algebraic structures nonlinear dynamic system can be represented as Lax pair and, in consequence, method of inverse dissipation problem to find solutions of the initial dynamical system [2] can be used
Summary
It is well known that solving the nonlinear partial equations is quite complicated procedure and the result can’t be ensured. That’s why it is important to find instruments that can propose quick answer for the question “Are these solving methods reasonable for application?” Method basing on existence of conservation laws of the initial dynamical system [1] can be used It is application of gradient-holonomic algorithm that makes possible to calculate hierarchy (in general case infinite) of conservation laws being attached to the algebraic structures. Wolf developed the package Con-Law 1-4 [5] (1999) in REDUCE language that was based on the solution of overdetermined partial differential equations system. This system needs some additional parameters to be calculated.
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