Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus
© 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved. A characteristic of the defocusing cubic nonlinear Schrödinger equation (NLSE), when defined so that the space variable is the multidimensional square (hence, rational) torus, is that there exist solutions that...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Society for Industrial & Applied Mathematics (SIAM)
2021
|
| Online Access: | https://hdl.handle.net/1721.1/135334 |
| _version_ | 1826215934695571456 |
|---|---|
| author | Staffilani, Gigliola Wilson, Bobby |
| author_facet | Staffilani, Gigliola Wilson, Bobby |
| author_sort | Staffilani, Gigliola |
| collection | MIT |
| description | © 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved. A characteristic of the defocusing cubic nonlinear Schrödinger equation (NLSE), when defined so that the space variable is the multidimensional square (hence, rational) torus, is that there exist solutions that start with arbitrarily small Sobolev norms and evolve to develop arbitrarily large modes at later times; this phenomenon is recognized as a weak energy transfer to high modes for the NLSE [Colliander et al., Invent. Math., 181 (2010), pp. 39{113] and [R. Carles and E. Faou, Discrete Contin. Dyn. Syst., 32 (2012), pp. 2063{2077]. In this paper, we show that when the system is considered on an irrational torus, energy transfer is more difficult to detect. |
| first_indexed | 2024-09-23T16:39:28Z |
| format | Article |
| id | mit-1721.1/135334 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:39:28Z |
| publishDate | 2021 |
| publisher | Society for Industrial & Applied Mathematics (SIAM) |
| record_format | dspace |
| spelling | mit-1721.1/1353342021-10-28T03:08:21Z Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus Staffilani, Gigliola Wilson, Bobby © 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved. A characteristic of the defocusing cubic nonlinear Schrödinger equation (NLSE), when defined so that the space variable is the multidimensional square (hence, rational) torus, is that there exist solutions that start with arbitrarily small Sobolev norms and evolve to develop arbitrarily large modes at later times; this phenomenon is recognized as a weak energy transfer to high modes for the NLSE [Colliander et al., Invent. Math., 181 (2010), pp. 39{113] and [R. Carles and E. Faou, Discrete Contin. Dyn. Syst., 32 (2012), pp. 2063{2077]. In this paper, we show that when the system is considered on an irrational torus, energy transfer is more difficult to detect. 2021-10-27T20:23:00Z 2021-10-27T20:23:00Z 2020 2021-06-01T15:52:09Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135334 en 10.1137/18M1179195 SIAM Journal on Mathematical Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial & Applied Mathematics (SIAM) SIAM |
| spellingShingle | Staffilani, Gigliola Wilson, Bobby Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title | Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title_full | Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title_fullStr | Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title_full_unstemmed | Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title_short | Stability of the Cubic Nonlinear Schrodinger Equation on an Irrational Torus |
| title_sort | stability of the cubic nonlinear schrodinger equation on an irrational torus |
| url | https://hdl.handle.net/1721.1/135334 |
| work_keys_str_mv | AT staffilanigigliola stabilityofthecubicnonlinearschrodingerequationonanirrationaltorus AT wilsonbobby stabilityofthecubicnonlinearschrodingerequationonanirrationaltorus |