Nonexistence of traveling waves for a nonlocal Gross-Pitaevskii equation
Andr\'e de Laire
TL;DR
This paper investigates a nonlocal Gross-Pitaevskii equation and establishes conditions under which traveling wave solutions do not exist for certain speeds, enhancing understanding of wave behavior in nonlocal quantum systems.
Contribution
It provides new sufficient conditions on the interaction potential that guarantee the nonexistence of traveling waves in specific speed ranges.
Findings
Traveling waves do not exist within certain speed intervals.
Sufficient conditions on the potential are identified for nonexistence.
Results contribute to the theoretical understanding of nonlocal quantum models.
Abstract
We consider a Gross-Pitaevskii equation with a nonlocal interaction potential. We provide sufficient conditions on the potential such that there exists a range of speeds in which nontrivial traveling waves do not exist
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Cold Atom Physics and Bose-Einstein Condensates