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0) (1,u) 6 R(uF(λ, 0)) holds;(H3) uF(λ,u) is a Fredholm operator of index zero whenever F(λ,u) = 0 with (λ,u) O;(H4) for ... It is therefore a Fredholm operator of index zero (see [6, Theorem 2.7.6]).

is. given by. π(HY ,T) = ind(T),. where ind(T) is the Fredholm index of T.

D. T.-R. McLaughlin, and A. Minakov. Soliton v.the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kineticequation arXiv:2205.02601, 2022.

SPECTRA OF GRAPH NEIGHBORHOODS AND SCATTERING. DANIEL GRIESER. Abstract. Let (Gε)ε>0 be a family of ’ε-thin’ Riemannian manifolds modeledon a finite metric graph G, for example, the ε-neighborhood of an embeddingof G in some Euclidean space

Dispersive hydrodynamics of soliton condensates forthe Korteweg-de Vries equation. T. Congy, G.A. El, G. Roberti, and A. Tovbis. Abstract. We consider large-scale dynamics of non-equilibrium dense soliton gas for theKorteweg-de Vries (KdV) equation

Soliton-mean field interaction in Korteweg-de Vriesdispersive hydrodynamics. Mark J. Ablowitz1, Justin T. Cole2, Gennady A. El3, Mark A. Hoefer1, andXu-dan Luo4. 1Department of Applied Mathematics, University of Colorado, Boulder2Department of

Soliton Gas: Theory, Numerics and Experiments. Pierre Suret,1, Stephane Randoux,1 Andrey Gelash,2 Dmitry Agafontsev,3, 4 Benjamin Doyon,5 and Gennady El4. 1Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules, F-59000 Lille

23 Jan 2004: that. ‖K‖ 14 ‖etÃF̃ etÃ‖h2 O(h3).(2.1)Therefore ‖K‖ scales with h2, rather than with h in standard applications ofNeumann expansions to, say, Fredholm equations of the second

12 Mar 2004: The Fredholm alternative theorem states that (52). has a solution only if the homogeneous problem,XNk0. ... then there would be innitely many solutions by the. Fredholm solvability theory.

21 May 2005: Prove the Fredholm alternative: Letλ R, λ 6= 0, and let x0 H.