Stability of Spatial Optical Solitons

Symmetric Plasmonic Slot Waveguides with a Nonlinear Dielectric Core: Bifurcations, Size Effects, and Higher Order Modes

“…The asymmetric nonlinear mode appears from the symmetric one through a symmetry-breaking bifurcation at a critical power. This bifurcation phenomenon has already been described in nonlinear slot waveguides, fully dielectric nonlinear waveguides, and waveguides made of nonlinear metal sandwiched between linear dielectrics 10,[12][13][14][15] .In this letter, we demonstrate the existence of a number of previously unknown higher order modes in the NSW. We show that bifurcations also occur for some of the higher order modes.…”

“…The asymmetric nonlinear mode appears from the symmetric one through a symmetry-breaking bifurcation at a critical power. This bifurcation phenomenon has already been described in nonlinear slot waveguides, fully dielectric nonlinear waveguides, and waveguides made of nonlinear metal sandwiched between linear dielectrics 10,[12][13][14][15] .…”

Uniqueness and stability of ground states for some nonlinear Schrödinger equations

“…In particular contexts such as (NLS), the relevance of (4.4) as a criterion for stability has been known at least since the work of Vakhitov-Kolokolov in 1973 ([15], [10]) and its rigorous justification for some cases of (NLS) was given by M. I. Weinstein [16], [13].…”

Existence and stability of TE modes in a stratified non-linear dielectric

“…There are extensive tables for the coefficients n 0 and n 2 (Smith, 1986). See also Kivshar & Sukhorukov (2001), Luther-Davies & Stegeman (2001) and the references in Stuart (1993) for a discussion of more general non-linearities. A medium is 'self-focusing' when ε(ω, x, s) is an increasing function of s.…”

“…However, these results are either of a perturbative nature (Grillakis et al, 1987;Strauss, 1989;Rose & Weinstein, 1988;Weinstein, 1986) and deal the solutions near the bifurcation point or they deal with a weaker notion of orbital stability (Cazenave & Lions (1982), Cazenave (2003), Hajaiej & Stuart (2004)). In a major contribution to the understanding of orbital stability, conditions were established in Grillakis et al (1987) giving a rigorous setting for the Vakhitov-Kolokolov (V-K) criterion (1973) (Kivshar & Sukhorukov, 2001). In our context, the V-K criterion states that u λ (x)e −iλτ is orbital stable if…”