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

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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 languageEnglish
Pages (from-to)1785-1800
Number of pages16
JournalMathematical Methods in the Applied Sciences
Volume29
Issue number15
DOIs
Publication statusPublished - Oct 1 2006
Externally publishedYes

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Wave Operator
Fourth Order
Nonlinearity
Scattering
Scattering Problems
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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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.",
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