An instability mechanism for radially symmetric standing waves of a nonlinear Schrödinger equation

DOI10.1016/0022-0396(88)90037-XzbMath0656.35108WikidataQ57925838 ScholiaQ57925838MaRDI QIDQ1109979

Christopher K. R. T. Jones

Publication date: 1988

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

dynamical systemsspectrumnonlinear Schrödinger equationspositive eigenvaluestanding waveargumentmultiple asymptotically positivenondegenerate waves

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (17)

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Cites Work

• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Stability theory for solitary-wave solutions of scalar field equations
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Instability of nonlinear bound states
• Existence of solitary waves in higher dimensions
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• On the existence and structure of stationary states for a nonlinear Klein-Gordon equation
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• On the Infinitely Many Solutions of a Semilinear Elliptic Equation
• A shooting argument with oscillation for semilinear elliptic radially symmetric equations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
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