Symmetry analysis of the bidimensional Lane-Emden systems
The paper addresses the system of Lane-Emden equations in two-dimensional space, which appear in astrophysics as models for the description of the intrinsic state of stars: \[ \Delta u + |v|^{q-1}v =0, \quad \Delta v + |u|^{q-1}u =0, \] where \(p\) and \(q\) are real constants (positive or negative). The paper reports on results of the analysis of the Noether symmetries and related conservation laws of this system. In particular, the dilation symmetry exists only along the curve \(p+q=-2\) (for \(p\neq-1\) and \(q\neq -1\)). This curve is simulataneously a critical one which separates the regions of existence and nonexistence of positive solutions to the system.
scientific article; zbMATH DE number 6009635
scientific article