Existence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in 3d

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Abstract

We study asymptotic behavior in time of solutions to nonlinear Schrödinger equations in three space dimensions with quadratic nongauge invariant nonlinearities. Due to the oscillation properties of such nonlinearities the time decay estimates are faster comparing with the case of guge invariant nonlinearities. We prove the existence of solutions to the final problem and large time asymptotics.

Keywords

Nonlinear Schrödinger equations , large time asymptotics
  • Nakao Hayashi Department of mathematics, Graduate School of Science Osaka. Toyonaka, 560-0043, Japan.
  • Pavel l. Naumkin Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 {Xangami), Morelia CP 58089, Michoacán, México.
  • Pages: 27–37
  • Date Published: 2007-04-01
  • Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal

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Published

2007-04-01

How to Cite

[1]
N. Hayashi and P. l. Naumkin, “Existence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in 3d”, CUBO, vol. 9, no. 1, pp. 27–37, Apr. 2007.

Issue

Vol. 9 No. 1 (2007): CUBO, A Mathematical Journal

Section

Articles