Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation |
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Authors: | DE Pelinovsky TV Phan |
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Institution: | 1. Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada;2. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, United States |
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Abstract: | We derive and justify a normal form reduction of the nonlinear Schrödinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form dynamics for both supercritical and subcritical pitchfork bifurcations in the time-dependent solutions of the nonlinear Schrödinger equation over long but finite time intervals. |
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