Normalized solutions of one-dimensional defocusing NLS equations with nonlinear point interactions

Abstract

We investigate normalized solutions for doubly nonlinear Schrödinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction of $\delta$-type at the origin. We provide a complete characterization of existence and uniqueness for normalized solutions and for energy ground states for every value of the nonlinearity powers. We show that the interplay between a defocusing standard and a focusing point nonlinearity gives rise to new phenomena with respect to those observed with single nonlinearities, standard combined nonlinearities, and combined focusing standard and pointwise nonlinearities.

25 pages, 1 figure. Keywords: doubly nonlinear Schrödinger, nonlinear point interactions, normalized solutions, ground states

References in corpus (23)

• Fast soliton scattering by delta impurities
• On Schroedinger Equations with Concentrated Nonlinearities
• The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications
• NLS ground states on metric graphs with localized nonlinearities
• Bound states of the NLS equation on metric graphs with localized nonlinearities
• Solitons supported by localized nonlinearities in periodic media
• On the lack of bound states for certain NLS equations on metric graphs
• Stability and symmetry-breaking bifurcation for the ground states of a NLS with a ${\delta }^{\prime }$ interaction
• Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
• Orbital and asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three
• $L^2$-critical NLS on noncompact metric graphs with localized nonlinearity: topological and metric features
• Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
• Orbital stability vs. scattering in the cubic-quintic Schrodinger equation
• On the 4D Nonlinear Schrödinger equation with combined terms under the energy threshold
• Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs
• The attractive nonlinear delta-function potential
• Instability of algebraic standing waves for nonlinear Schrödinger equations with double power nonlinearities
• Blow-up for the pointwise NLS in dimension two: absence of critical power
• Singular mean-field states: A brief review of recent results
• Blow-up and instability of standing waves for the NLS with a point interaction in dimension two
• NLS ground states on the half-line with point interactions
• Stability of the standing waves of the concentrated NLSE in dimension two
• Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one