Dispersion managed solitons in the presence of saturated nonlinearity

Hundertmark, Dirk; Lee, Young Ran; Ried, Tobias; Zharnitsky, Vadim

doi:10.1016/j.physd.2017.06.004

Cited by 9 publications

(2 citation statements)

References 17 publications

(28 reference statements)

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“…Inspired [22,25], we introduce the PSP condition, which is a weaker compactness condition than the standard Palais-Smale one. Such (PSP) condition takes into account the scaling properties of I through the Pohozaev functional P. Using this new condition we will show that K PSP b is compact when b < 0.…”

Section: Palais-smale-pohozaev Conditionmentioning

confidence: 99%

Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

2021

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We study existence of solutions for the fractional problem ( P m ) ( − Δ ) s u + μ u = g ( u ) in R N , ∫ R N u 2 d x = m , u ∈ H r s ( R N ) , where N ⩾ 2, s ∈ (0, 1), m > 0, μ is an unknown Lagrange multiplier and g ∈ C ( R , R ) satisfies Berestycki–Lions type conditions. Using a Lagrangian formulation of the problem (P m ), we prove the existence of a weak solution with prescribed mass when g has L 2 subcritical growth. The approach relies on the construction of a minimax structure, by means of a Pohozaev’s mountain in a product space and some deformation arguments under a new version of the Palais–Smale condition introduced in Hirata and Tanaka (2019 Adv. Nonlinear Stud. 19 263–90); Ikoma and Tanaka (2019 Adv. Differ. Equ. 24 609–46). A multiplicity result of infinitely many normalized solutions is also obtained if g is odd.

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Section: Palais-smale-pohozaev Conditionmentioning

confidence: 99%

Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation

2021

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“…We refer Combes-Hislop-Klopp [38], Combes-Hislop [3], Hundertmark-Killip-Nakamura-Stollmann-Veselić [16], Kirsch [10], Kirsch-Veselic [11] and Stollmann [6] for more about Wegner estimate. To perform multiscale analysis in the region (−∞, 0), we need the Wegner estimate for small enough interval around E for any E ∈ (−∞, 0).…”

Section: Introductionmentioning

confidence: 99%

Schrödinger operators with decaying randomness - Pure point spectrum

Mallick,

Dolai

2018

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For Schrödinger operator with decaying random potential with fat tail single site distribution the negative spectrum shows a transition from essential spectrum to discrete spectrum. We study the Schrödinger operatorHere we take a n = O(|n| −α ) for large n where α > 0, and {ω n } n∈Z d are i.i.d real random variables with absolutely continuous distribution µ such that dµ dx (x) = O |x| −(1+δ) as |x| → ∞, for some δ > 0. We show that H ω exhibits exponential localization on negative part of spectrum independent of the parameters chosen. For αδ ≤ d we show that the spectrum is entire real line almost surely, but for αδ > d we have σ ess (H ω ) = [0, ∞) and negative part of the spectrum is discrete almost surely. In some cases we show the existence of the absolutely continuous spectrum.

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