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Traveling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension one

Abstract : We study the traveling waves of the Nonlinear Schrödinger Equation in dimension one. Through various model cases, we show that for nonlinearities having the same qualitative behaviour as the standard Gross-Pitaevkii one, the traveling waves may have rather different properties. In particular, our examples exhibit multiplicity or nonexistence results, cusps (as for the Jones-Roberts curve in the three-dimensional Gross-Pitaevskii equation), and a transonic limit which can be the modified (KdV) solitons or even the generalized (KdV) soliton instead of the standard (KdV) soliton.
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David Chiron. Traveling waves for the Nonlinear Schrödinger Equation with general nonlinearity in dimension one. Nonlinearity, IOP Publishing, 2012, 25 (3), pp.813-850. ⟨10.1088/0951-7715/25/3/813⟩. ⟨hal-00809123⟩

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