Abstract:

Using Legendre singularity theory, we studied the local bifurcations of completely integrable holonomic systems of 2variable firstorder nonlinearity partial differential equations whose corresponding oneparameter integral diagrams are R⁺simple and stable so as to obtain the classification of local bifurcations. Based on the result, the qualitative state of this system can be estimated when the parameters are changed.

Key words:  Legendre singularity theory, 2variable firstorder non-linearity partial differential equation, local bifurcation, classification