# Long range scattering for nonlinear Schrödinger equations in one and two space dimensions

@inproceedings{Akihiro2003LongRS, title={Long range scattering for nonlinear Schr{\"o}dinger equations in one and two space dimensions}, author={Akihiro and Satoshi}, year={2003} }

- Published 2003

We study the scattering theory for the nonlinear Schrödinger equations with cubic and quadratic nonlinearities in one and two space dimensions, respectively. For example, the nonlinearities are sum of gauge invariant term and non-gauge invariant terms such as λ0|u|2u + λ1u + λ2uū + λ3ū in one dimensional case, where λ0 ∈ R and λ1, λ2, λ3 ∈ C. The scattering theory for these equations belongs to the long range case. We show the existence and uniqueness of global solutions for those equations… CONTINUE READING

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