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- W2053290411 abstract "A new family of defect solutions to the nonlinear Schrodinger equation is described. The defects have standing wave dynamics with j concentric rings centered at the defect site r=0, and a conical shape as rensuremath{rightarrow}0 with angle of opening ${mathrm{ensuremath{varphi}}}_{mathit{j}}$. Using a phase space technique, solution trajectories having a prescribed number (j) of rings are computed along with their corresponding eigenvalue ${ensuremath{nu}}_{mathit{j}}$, and angle of opening ${mathrm{ensuremath{varphi}}}_{mathit{j}}$. As in the linear Sturm-Liouville theory, the eigenvalues are ordered so that ${ensuremath{nu}}_{mathit{j}mathrm{ensuremath{-}}1}$${ensuremath{nu}}_{mathit{j}}$${ensuremath{nu}}_{mathit{j}+1}$, a fact which is clearly seen from the phase space structure. The nonlinear eigenfunctions are trajectories which lie on the basin boundary between the domains of the attraction of the two asymptotically stable trajectories in the three dimensional phase space. The asymptotic distribution of the eigenvalues for large j, and the angle of opening at the defect site are both shown to have a power law form, and formulas for the power law exponents are given. textcopyright{} 1996 The American Physical Society." @default.
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- W2053290411 date "1996-04-01" @default.
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- W2053290411 title "Scaling laws at nonlinear Schrödinger defect sites" @default.
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- W2053290411 doi "https://doi.org/10.1103/physreve.53.3442" @default.
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