Threshold odd solutions to the nonlinear Schrödinger equation in one dimension

Stephen Gustafson () and Takahisa Inui ()
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Stephen Gustafson: University of British Columbia
Takahisa Inui: University of British Columbia

Partial Differential Equations and Applications, 2022, vol. 3, issue 4, 1-45

Abstract: Abstract We consider odd solutions to the Schrödinger equation with the $$L^{2}$$ L 2 -supercritical power type nonlinearity in one dimensional Euclidean space. It is known that the odd solution scatters or blows up if its action is less than twice that of the ground state. In the present paper, we show that odd solutions with action twice that of the ground state scatter or blow up.

Keywords: Nonlinear Schrödinger equation; Odd functions; Global dynamics; Threshold; 35Q55; 37K40 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00183-2

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