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Limit at infinity and nonexistence results for sonic travelling waves in the Gross-Pitaevskii equation. (English) Zbl 1150.35301
Summary: We study the limit at infinity of sonic travelling waves of finite energy in the Gross-Pitaevskii equation in dimension $$N\geq 2$$ and prove the nonexistence of nonconstant sonic travelling waves of finite energy in dimension two.

##### MSC:
 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B40 Asymptotic behavior of solutions to PDEs 35Q55 NLS equations (nonlinear Schrödinger equations)
##### Keywords:
Gross-Pitaevskii equation; travelling waves; nonexistence