Bifurcations of completely integrable 2-variable first-order partial differential equations
The authors consider an implicit 2-variable first-order partial differential equations \[ F(x_{1}, x_{2}, y, \frac{dy}{dx_{1}}, \frac{dy}{dx_{2}})=0, \] where \(F\) is a sufficiently smooth function and \(0\) is its regular value, i.e., \(F^{-1}(0)\) is a \(3D\) submanifold of \(J^{1}(\mathbb{R}^{2},\mathbb{R})\) (1-jet bundle of 2-variable function). By using Legendrian singularity theory, here, the generic classification is given for bifurcations of such differential equations with respect to the equivalence relation determined by the Lie group of point transformations.
scientific article; zbMATH DE number 5909845