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- W1784645286 abstract "Abstract The system describes pulses in nonlinear fiber couplers. It has the family (U 1+λ , -U 1+λ ), -1 < λ < ∞, of soliton states (that is, homoclinic solutions to the origin), where For λ ≥ 1, the equilibrium (0, 0) is not hyperbolic and therefore the soliton state (U 1+λ , −U 1+λ ) can be qualified as “singular”. In N. Akhmediev and A. Ankiewicz [1], it is observed numerically that a branch of homoclinic solutions bifurcates subcritically at λ = 1 from the family (U 1+λ , −U 1+λ ). The aim of the present paper is to give a rigorous proof of the existence of this bifurcation, as desired in A. Ambrosetti and D. Arcoya [3]. A particular feature of the present problem is that the linearized system at (U 2 , −U 2 ) has a non-constant bounded solution that does not vanish at infinity. Hence the bifurcating homoclinic solutions have a transient “spatial” region where they are well described with the help of this bounded function. Moreover the decay to 0 is governed by two different scales, the larger one originating from the singular aspect of (U 2 , −U 2 ). The existence proof developed here relies on the “broken geodesic” technique to match the inside transient region with the outside region." @default.
- W1784645286 created "2016-06-24" @default.
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- W1784645286 date "2012-11-01" @default.
- W1784645286 modified "2023-10-03" @default.
- W1784645286 title "Bifurcation Analysis at a Singular Soliton State in Fiber Couplers" @default.
- W1784645286 cites W2012203520 @default.
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- W1784645286 doi "https://doi.org/10.1515/ans-2012-0405" @default.
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