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• W2060401038 abstract "is studied for the four cases; (p = 1, s = 1), (p = 1, s = −1), (p = −1, s = −1) and (p = −1, s = 1). Solitary waves in the x-direction are envelopes ψ = √2 sech(x) exp (it), for p = 1, and they are kinks; ψ = √2 tanh(x) exp (– 2it), for p = −1. For s = 1 an energy principle can be invoked, and instability for the envelope occurs in the range 0 < k2 < 3, and for the kink in the range 0 < k2 < 1. Here k is the wavenumber of the perturbation in the y-direction. Growth rates are estimated very simply by means of a Rayleigh-Ritz method. For s = −1, we review existing results for the envelope. It is unstable in a range 0 < k2 ⩽ 1.17 where the upper limit must be determined numerically. For the kink, we find a continuum of unstable, non-local perturbations covering the whole range 0 < k2 < ∞. On both sides of the kink structure (|x| ≫ 1) these perturbations are oblique, purely growing plane waves." @default.
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• W2060401038 date "1989-08-01" @default.
• W2060401038 modified "2023-10-15" @default.
• W2060401038 title "Stability of solitary structures in the nonlinear Schrödinger equation" @default.
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• W2060401038 doi "https://doi.org/10.1088/0031-8949/40/2/008" @default.
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