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math.AP2008★ 2 cited
On the KP I transonic limit of two-dimensional Gross-Pitaevskii travelling waves
Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut
We provide a rigorous mathematical derivation of the convergence in the long-wave transonic limit of the minimizing travelling waves for the two-dimensional Gross-Pitaevskii equati…
math.AP2008★ 61 cited
Orbital stability of the black soliton to the Gross-Pitaevskii equation
Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut +1
We establish the orbital stability of the black soliton, or kink solution, $\v_0(x) = þ\big(\frac{x}{\sqrt{2}} \big)$, to the one-dimensional Gross-Pitaevskii equation, with respec…