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2012•Indiana University Mathematics JournalRequires access

On instability for the quintic nonlinear Schrodinger equation of some approximate periodic solutions

Jeremy L. Marzuola, Scipio Cuccagna

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Abstract

Using the Fermi Golden Rule analysis developed in (CM), we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrodinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrodinger Equation (NLSE) with symmetric po- tential in (MW) do not persist in the comparable quintic NLSE.

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What this paper is about

Using the Fermi Golden Rule analysis developed in (CM), we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrodinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrodinger Equation (NLSE) with symmetric po- tential in (MW) do not persist in the comparable quintic NLSE.

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Available abstract

Using the Fermi Golden Rule analysis developed in (CM), we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrodinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrodinger Equation (NLSE) with symmetric po- tential in (MW) do not persist in the comparable quintic NLSE.

Key concepts: Quintic function, Mathematics, Instability, Nonlinear Schrödinger equation, Nonlinear system, Mathematical analysis, Schrödinger equation, Applied mathematics

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