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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)
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