Stability of Standing Waves for the Logarithmic Schrödinger Equation with Attractive Delta Potential

Stability of Standing Waves for the Logarithmic Schrödinger Equation with Attractive Delta Potential

We consider the one-dimensional logarithmic Schrödinger equation with a delta potential. Global well-posedness is verified for the Cauchy problemin H¹(ℝ) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.

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Veröffentlicht in:Indiana University mathematics journal 2018-01, Vol.67 (2), p.471-494
Hauptverfasser: Pava, Jaime Angulo, Ardila, Alex Hernandez
Format: Artikel
Sprache:eng
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Zusammenfassung:We consider the one-dimensional logarithmic Schrödinger equation with a delta potential. Global well-posedness is verified for the Cauchy problemin H¹(ℝ) and in an appropriate Orlicz space. In the attractive case, we prove orbital stability of the ground states via variational approach.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2018.67.7273