Bifurcations of completely integrable 2-variable first-order partial differential equations |
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Authors: | Jingbo Xu Liang Chen |
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Institution: | a School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, PR China b School of Mathematics, Jilin Normal University, Siping 136000, PR China c Changchun University of Science and Technology, Changchun 130022, PR China |
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Abstract: | In this paper, we consider an implicit 2-variable first-order partial differential equation with complete integral. As an application of the Legendrian singularity theory, we give a generic classification of bifurcations of such differential equations with respect to the equivalence relation which is given by the group of point transformations following S. Lie?s view. Since two one-parameter unfoldings of such differential equations are equivalent if and only if induced one-parameter unfoldings of integral diagrams are equivalent for generic equations, our normal forms are represented by one-parameter integral diagrams. |
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Keywords: | Legendrian singularity Bifurcation First-order differential equation Complete integral |
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