Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion
Résumé
In this note we provide some simple results for the 4NLS model i∂tψ + ∆ψ + |ψ| 2σ ψ − γ∆ 2 ψ = 0, where γ > 0. Our aim is to partially complete the discussion on waveguide solutions in [11, Section 4.1]. In particular, we show that in the model case with a Kerr nonlinearity (σ=1), the least energy waveguide solution ψ(t, x) = exp(iαt)u(x) with α > 0 is unique for small γ and qualitatively behaves like the waveguide solution of NLS. On the contrary, oscillations arise at infinity when γ is too large.
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