Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity

Junichi Segata

doi:10.1002/mma.751

Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity

Junichi Segata

Research output: Contribution to journal › Article › peer-review

46 Citations (Scopus)

Abstract

We consider the scattering problem for the fourth-order non-linear Schrödinger-type equation: i∂_tu - 1/4∂ _x⁴u = λ|u|^p-1u, t, x ∈ R We show the existence of the modified wave operators for the above equation with cubic case by imposing the mean zero condition for the final data.

Original language	English
Pages (from-to)	1785-1800
Number of pages	16
Journal	Mathematical Methods in the Applied Sciences
Volume	29
Issue number	15
DOIs	https://doi.org/10.1002/mma.751
Publication status	Published - Oct 1 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Engineering(all)

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10.1002/mma.751

Cite this

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title = "Modified wave operators for the fourth-order non-linear Schr{\"o}dinger-type equation with cubic non-linearity",

abstract = "We consider the scattering problem for the fourth-order non-linear Schr{\"o}dinger-type equation: i∂tu - 1/4∂ x4u = λ|u|p-1u, t, x ∈ R We show the existence of the modified wave operators for the above equation with cubic case by imposing the mean zero condition for the final data.",

author = "Junichi Segata",

year = "2006",

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AB - We consider the scattering problem for the fourth-order non-linear Schrödinger-type equation: i∂tu - 1/4∂ x4u = λ|u|p-1u, t, x ∈ R We show the existence of the modified wave operators for the above equation with cubic case by imposing the mean zero condition for the final data.

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Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity

Abstract

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