On the formation of singularities of solutions of nonlinear differential systems in antistokes directions
By O. Costin, R. Costin. 2001
87 citations recorded by the source corpus.
We determine the position and the type of spontaneous singularities of solutions of generic analytic nonlinear differential systems in the complex plane, arising along antistokes directions towards irregular singular points of the system. Placing the singularity of the system at infinity we look at equations of the form $\mathbf{y}'=\mathbf{f}(x^{-1},\mathbf{y})$ with $\mathbf{f}$ analytic in a neighborhood of $(0,\mathbf{0})$, with genericity assumptions; $x=\infty$ is then a rank one singular point. We analyze the singularities of those solutions $\mathbf{y}(x)$ which tend to zero for $x\to \infty$ in some sectorial region, on the edges of the maximal region (also described) with this property. After standard normalization of the differential system, it is shown that singularities occuring in antistokes directions are grouped in nearly periodical arrays of similar singularities as $x\to\infty$, the location of the array depending on the solution while the (near-) period and type of singularity are determined by the form of the differential system.
Subfields: Applied Mathematics, Geometry and Topology, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/10840efd2386fc7d5216503d4cc49bb7b51c6683
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Numerical Analysis
Citations in the corpus
- Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings (2012, background): “In fact, the same situation arises in non-linear ODEs, where this leads to the formation of singularities along anti–Stokes lines, see for example [40].”