Method of general Сoule-Hopf substitutions in theory of finite-dimensional dynamical systems

Abstract


We consider the results of applying the method of generic Cole-Hopf substitutions to integration of finite-dimensional dynamical systems. Dynamical systems are represented in the form of matrix ordinary differential equations with specific matrix algebra of finite dimension. The Cole-Hopf type substitutions are applied to matrix equations by using the differentiation on algebra in the form of commutator with a specific algebra element. Recurrent relations for Cole-Hopf substitutions were found. Particular cases of exactly integrable dynamical systems are presented. The algorithm of calculating the integrals of motion is shown.

About the authors

Victor M Zhuravlev

Ulyanovsk State University

Email: zhvictorm@gmail.com
д.ф.-м.н., проф., профессор, каф. теоретической физики; Ульяновский государственный университет; Ulyanovsk State University

Konstantin S Obrubov

Ulyanovsk State University

Email: constantin.phys@gmail.com
аспирант, каф. теоретической физики; Ульяновский государственный университет; Ulyanovsk State University

References

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