Wave and inverse wave operators for the quadratic nonlinear Schrödinger equations in 3D
Kawahara, Yuichiro
Osaka J. Math., Tome 44 (2007) no. 1, p. 909-921 / Harvested from Project Euclid
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Our purpose in this paper is to prove existence of wave operator $\mathcal{W}_{+}$ or inverse wave operator $\widetilde{\mathcal{W}}_{+}$ for nonlinear Schrödinger equations with quadratic nonlinearities in three space dimensions. Our results show that the mapping $\mathcal{W}_{+} \widetilde{\mathcal{W}}_{+}$ is well defined and are improvement of results on the range of inverse wave operator obtained in [6].
Publié le : 2007-12-15
Classification:  35Q55,  35B40 
@article{1199719412,
     author = {Kawahara, Yuichiro},
     title = {Wave and inverse wave operators for the quadratic nonlinear Schr\"odinger equations in 3D},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 909-921},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1199719412}
}

Kawahara, Yuichiro. Wave and inverse wave operators for the quadratic nonlinear Schrödinger equations in 3D. Osaka J. Math., Tome 44 (2007) no. 1, pp.  909-921. http://gdmltest.u-ga.fr/item/1199719412/