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}
}
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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References

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Showing 1-10 of 34 references

Existence of solutions for Schrödinger evolution equations

K. Yajima
Comm. Math. Phys., 110 • 2003
View 5 Excerpts
Highly Influenced

Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension n ≥ 2

J. Ginibre, T. Ozawa
Comm. Math. Phys., 151 • 1993
View 7 Excerpts
Highly Influenced

Long range scattering for nonlinear Schrödinger equations in one space dimension

T. Ozawa
Comm. Math. Phys., 139 • 1991
View 10 Excerpts
Highly Influenced

A scattering theory for time-dependent long-range potentials

H. Kitada, K. Yajima
Duke Math. J., 49 • 1982
View 4 Excerpts
Highly Influenced

Nonexistence of asymptotically free solutions for nonlinear Schrödinger equations

J. E. Barab
J. Math. Phys., 25 • 1984
View 4 Excerpts
Highly Influenced

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