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Lie group analysis of two-dimensional variable-coefficient Burgers equation

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Abstract

The modern group analysis of differential equations is used to study a class of two-dimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are also found that allow us to simplify the results of classification and to construct the basis of differential invariants and operators of invariant differentiation. Using equivalence transformations, reductions with respect to Lie symmetry operators and certain non-Lie ansätze, we construct exact analytical solutions for specific forms of the arbitrary elements. Finally, we classify the local conservation laws.

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Authors and Affiliations

  1. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., 01601, Kiev, Ukraine

    N. M. Ivanova

  2. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus

    N. M. Ivanova & C. Sophocleous

  3. Department of Mathematics and Computer Science, University of Catania, Catania, Italy

    R. Tracinà

Authors
  1. N. M. Ivanova
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  2. C. Sophocleous
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  3. R. Tracinà
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Correspondence to C. Sophocleous.

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Ivanova, N.M., Sophocleous, C. & Tracinà, R. Lie group analysis of two-dimensional variable-coefficient Burgers equation. Z. Angew. Math. Phys. 61, 793–809 (2010). https://doi.org/10.1007/s00033-009-0053-8

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  • DOI: https://doi.org/10.1007/s00033-009-0053-8

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