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A non-existence result for supersonic travelling waves in the Gross-Pitaevskii equation. (English) Zbl 1044.35087
Summary: We prove the non-existence of non-constant travelling waves of finite energy and of speed \(c>\sqrt2\) in the Gross-Pitaevskii equation \[ i\partial_t u=\Delta u+u(1-| u|^2) \] in dimension \(N\geq2\).

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35J60 Nonlinear elliptic equations
35Q40 PDEs in connection with quantum mechanics
35Q51 Soliton equations
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