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Nonlocal symmetries of evolution equations

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Abstract

We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution equations in one spatial variable invariant under Lie algebras of the dimension up to three. As a result, we construct the broad families of new nonlinear evolution equations possessing nonlocal symmetries which in principle cannot be obtained within the classical Lie approach.

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  1. BIO-key International, Eagan, MN, 55121, USA

    Renat Zhdanov

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  1. Renat Zhdanov
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Correspondence to Renat Zhdanov.

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Zhdanov, R. Nonlocal symmetries of evolution equations. Nonlinear Dyn 60, 403–411 (2010). https://doi.org/10.1007/s11071-009-9604-y

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  • DOI: https://doi.org/10.1007/s11071-009-9604-y

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