For NLS on a strip with an attractive delta interaction, line solitons are orbitally stable below a critical width and unstable above, with a pitchfork branch of new positive solutions at the threshold.
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Transverse Instability and Bifurcation Analysis of the line soliton for the NLS equation on a Fractured Strip
For NLS on a strip with an attractive delta interaction, line solitons are orbitally stable below a critical width and unstable above, with a pitchfork branch of new positive solutions at the threshold.