Ufa Mathematical Journal
    Volume 9, Number 4, pp. 108-113

    On differential substitutions for evolution systems

    Startsev S.Ya.


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    We obtain necessary and sufficient conditions for a differential substitution to be admitted by a family of evolution systems that depends on an arbitrary function. As an illustration, such family is constructed for a multi-component Cole-Hopf substitution and we demonstrate that this family contains all linear systems the right-hands sides of which do not depend on the derivatives of order less than one. As a result, a family of C-integrable systems of arbitrary high order is obtained.