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Remarks on solitary waves and Cauchy problem for Half-wave-Schrödinger equations.
- Source :
- Communications in Contemporary Mathematics; Aug2021, Vol. 23 Issue 5, pN.PAG-N.PAG, 31p
- Publication Year :
- 2021
-
Abstract
- In this paper, we study solitary wave solutions of the Cauchy problem for Half-wave-Schrödinger equation in the plane. First, we show the existence and the orbital stability of the ground states. Second, we prove that given any speed v , traveling wave solutions exist and converge to the zero wave as the velocity tends to 1. Finally, we solve the Cauchy problem for initial data in L x 2 H y s (ℝ 2) , with s > 1 2 . The critical case s = 1 2 still stands as an interesting open problem. [ABSTRACT FROM AUTHOR]
- Subjects :
- PROBLEM solving
EQUATIONS
SCHRODINGER equation
CAUCHY problem
STANDING waves
Subjects
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 23
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 151524218
- Full Text :
- https://doi.org/10.1142/S0219199720500583