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タイトル: | Stability of Algebraic Solitons for Nonlinear Schrödinger Equations of Derivative Type: Variational Approach |
著者: | HAYASHI, Masayuki |
著者名の別形: | 林, 雅行 |
キーワード: | 35A15 35Q51 35Q55 35B35 derivative nonlinear Schrödinger equation solitons variational methods orbital stability |
発行日: | Oct-2020 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
開始ページ: | 1 |
終了ページ: | 24 |
論文番号: | RIMS-1929 |
抄録: | We consider the following nonlinear Schrödinger equation of derivative type: (1) i∂tu + ∂2x u + i|u|2∂xu + b|u|4u = 0, (t, x) ∈ R×R, b ∈ R. If b = 0, this equation is a gauge equivalent form of well-known derivative nonlinear Schrödinger (DNLS) equation. The equation (1) can be considered as a generalized equation of (DNLS) while preserving both L2-criticality and Hamiltonian structure. If b > -3/16, the equation (1) has algebraically decaying solitons, which we call algebraic solitons, as well as exponentially decaying solitons. In this paper we study stability properties of solitons for (1) by variational approach and prove that if b < 0, all solitons including algebraic solitons are stable in the energy space. The stability of algebraic solitons gives the counterpart of the previous instability result for the case b > 0. |
URI: | http://hdl.handle.net/2433/261827 |
関連リンク: | http://www.kurims.kyoto-u.ac.jp/preprint/index.html |
出現コレクション: | 数理解析研究所プレプリント |
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