ratkaisunDifferentiaaliyhtälöille
RatkaisunDiffe is a theoretical framework in the analysis of differential equations that uses smooth transformations to study the structure of solution spaces. The name blends the Finnish word ratkaisun with diffe from diffeomorphism, signaling a focus on solution-level equivalences under diffeomorphisms.
The framework treats sets of solutions as differentiable manifolds or stratified spaces, with a group of diffeomorphisms
Core ideas include: using diffeomorphisms to map complex equations to simpler equivalents; describing solution families by
Applications include qualitative analysis of nonlinear ordinary and partial differential equations, symmetry reductions to lower-dimensional problems,
Status: RatkaisunDiffe is largely a conceptual and methodological area without a single unified framework, cited mainly