A DEGENERATE EDGE BIFURCATION IN THE 1D LINEARIZED NONLINEAR SCHRODINGER EQUATION

被引：6

作者：

Coles, Matt ^{[1
]}

Gustafson, Stephen ^{[1
]}

机构：

[1] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Nonlinear Schrodinger equation; linearized operator; edge bifurcation; Birman-Schwinger formulation; resolvent expansion; Lyapunov-Schmidt reduction; ASYMPTOTIC STABILITY; SOLITARY WAVES; GROUND-STATES; EVANS FUNCTION; NLS EQUATION; EIGENVALUES; RESONANCES; OPERATORS; SOLITONS; SPECTRA;

D O I：

10.3934/dcds.2016.36.2991

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work deals with the focusing Nonlinear Schrodinger Equation in one dimension with pure-power nonlinearity near cubic. We consider the spectrum of the linearized operator about the soliton solution. When the nonlinearity is exactly cubic, the linearized operator has resonances at the edges of the essential spectrum. We establish the degenerate bifurcation of these resonances to eigenvalues as the nonlinearity deviates from cubic. The leading order expression for these eigenvalues is consistent with previous numerical computations.

引用

页码：2991 / 3009

页数：19

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