Asymptotic solutions of an elliptic equation system on a Riemannian manifold concentrated in the vicinity of a phase trajectory
V. S. Buldyrev, V. E. Nomofilov · Journal of Physics A Mathematical and General · 1981
The scalar Helmholtz equation has solutions concentrated in a small vicinity of a ray. Outside this vicinity these solutions decrease exponentially. Solutions with similar features are constructed for an elliptic equation system and examples such as the linear problems of elasticity theory, crystallo-optics, magnetic hydrodynamics and gravitation theory are given.