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Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation

In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schrödinger-Kirchhoff equation. The presence of a mixed term gives us more dispersion, and consequently, a different scenario for the stability of solitary waves in contrast with the corresponding nonlinear Schrödinger equation. For periodic waves, we exhibit two explicit solutions and prove the orbital stability in the energy space.

preprint2020arXivOpen access
Fábio NataliEleomar Cardoso Jr
math.AP
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Open access2 authors1 topic
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Fábio NataliEleomar Cardoso Jr

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