Persistent Homoclinic Orbits for Nonlinear Schrödinger Equation Under Singular Perturbation

@inproceedings{Li2008PersistentHO,
  title={Persistent Homoclinic Orbits for Nonlinear Schr{\"o}dinger Equation Under Singular Perturbation},
  author={Yanguang Li},
  year={2008}
}
Existence of homoclinic orbits in the cubic nonlinear Schrödinger equation under singular perturbations is proved. Emphasis is placed upon the regularity of the semigroup eǫt∂ 2 x at ǫ = 0. This article is a substantial generalization of [3], and motivated by the effort of Dr. Zeng [9] [8]. The mistake of Zeng in [8] is corrected with a normal form transform approach. Both one and two unstable modes cases are investigated. 

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