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Numerical analyses for spectral stability of solitary waves near bifurcation points

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Abstract

We present a numerical approach for determination of the spectral stability of solitary waves by computing eigenvalues and eigenfunctions of the corresponding eigenvalue problems, along with their continuation, for nonlinear wave equations in one space dimension. We illustrate the approach for the nonlinear Schrödinger (NLS) equation with a small potential, and numerically determine the spectral stability of solitary waves near bifurcation points along with computations of eigenfunctions and eigenvalues. The numerical results demonstrate some theoretical ones the authors recently obtained for the example.

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Authors and Affiliations

  1. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Kazuyuki Yagasaki & Shotaro Yamazoe

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  1. Kazuyuki Yagasaki
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  2. Shotaro Yamazoe
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Correspondence to Kazuyuki Yagasaki.

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This work was partially supported by JSPS KAKENHI Grant Number JP17H02859.

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Yagasaki, K., Yamazoe, S. Numerical analyses for spectral stability of solitary waves near bifurcation points. Japan J. Indust. Appl. Math. 38, 125–140 (2021). https://doi.org/10.1007/s13160-020-00428-w

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  • DOI: https://doi.org/10.1007/s13160-020-00428-w

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