Persistent Homoclinic Orbits for Nonlinear Schroedinger Equation Under Singular Perturbation
Yanguang Charles Li
Abstract
Existence of homoclinic orbits in the cubic nonlinear Schrödinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup e t x2 at = 0. This article is a substantial generalization of LMSW96, and motivated by the effort of Dr. Zeng Zen00a Zen00b. The mistake of Zeng in Zen00b is corrected with a normal form transform approach. Both one and two unstable modes cases are investigated.
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