Geodesic
Nonlinearity-defect interaction: symmetry breaking bifurcation in a NLS with a $\delta$' impurity
Nanosistemy: fizika, himiâ, matematika, Tome 2 (2011) no. 4, pp. 5-19.

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We illustrate some new results and comment on perspectives of a recent research line, focused on the stability of stationary states of nonlinear NLS with point interactions. We describe in detail the case of a "$\delta'$" interaction, that provides a rich model endowed with a pitchfork bifurcation with symmetry breaking in the family of ground states. Finally, we give a direct proof of the stability of the ground states in the cases of a subcritical and critical (in the sense of the blow-up) nonlinearity power.
Keywords: nonlinear dynamics, quantum mechanics, symmetry breaking, pitchfork bifurcation.
Mots-clés : solitons 
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     author = {R. Adami and D. Noja},
     title = {Nonlinearity-defect interaction: symmetry breaking bifurcation in a {NLS} with a $\delta$' impurity},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
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     publisher = {mathdoc},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2011_2_4_a0/}
}
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R. Adami; D. Noja. Nonlinearity-defect interaction: symmetry breaking bifurcation in a NLS with a $\delta$' impurity. Nanosistemy: fizika, himiâ, matematika, Tome 2 (2011) no. 4, pp. 5-19. http://geodesic.mathdoc.fr/item/NANO_2011_2_4_a0/