A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up

F. Güngör; M. Hasanov; C. Özemir

doi:10.1080/00036811.2012.676165

A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up

F. Güngör^*
, M. Hasanov
, C. Özemir

^*Corresponding author for this work

Department of Mathematics Engineering

Dogus University

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

2 Citations (Scopus)

Abstract

A canonical variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the L _p-norm for p > 2, L _∞-norm and in the sense of distributions.

Original language	English
Pages (from-to)	1322-1331
Number of pages	10
Journal	Applicable Analysis
Volume	92
Issue number	6
DOIs	https://doi.org/10.1080/00036811.2012.676165
Publication status	Published - Jun 2013

Keywords

SL(2, ℝ) invariance
blow-up
exact solutions
variable coefficient nonlinear Schrödinger equation

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10.1080/00036811.2012.676165

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abstract = "A canonical variable coefficient nonlinear Schr{\"o}dinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlev{\'e} expansion and study blow-ups of these solutions in the L p-norm for p > 2, L ∞-norm and in the sense of distributions.",

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N2 - A canonical variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the L p-norm for p > 2, L ∞-norm and in the sense of distributions.

AB - A canonical variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group containing SL(2, ℝ) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the L p-norm for p > 2, L ∞-norm and in the sense of distributions.

KW - SL(2, ℝ) invariance

KW - blow-up

KW - exact solutions

KW - variable coefficient nonlinear Schrödinger equation

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DO - 10.1080/00036811.2012.676165

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SP - 1322

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JF - Applicable Analysis

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ER -

A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up

Abstract

Keywords

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