Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems
We consider the nonlinear Schrodinger systems $$displaylines{ -ipartial _tu_1+frac{1}{2}Delta u_1=F( u_1,u_2), cr ipartial _tu_2+frac{1}{2}Delta u_2=F( u_1,u_2) }$$ in n space dimensions, where F is a p-th order local or nonlocal nonlinearity smooth up to order p, with $1<pleq 1+frac{2}...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2012-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/162/abstr.html |
| _version_ | 1818178066669633536 |
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| author | Nakao Hayashi Chunhua Li Pavel I. Naumkin |
| author_facet | Nakao Hayashi Chunhua Li Pavel I. Naumkin |
| author_sort | Nakao Hayashi |
| collection | DOAJ |
| description | We consider the nonlinear Schrodinger systems $$displaylines{ -ipartial _tu_1+frac{1}{2}Delta u_1=F( u_1,u_2), cr ipartial _tu_2+frac{1}{2}Delta u_2=F( u_1,u_2) }$$ in n space dimensions, where F is a p-th order local or nonlocal nonlinearity smooth up to order p, with $1<pleq 1+frac{2}{n}$ for $ngeq 2$ and $1<pleq 2$ for n=1. These systems are related to higher order nonlinear dispersive wave equations. We prove the non existence of asymptotically free solutions in the critical and sub-critical cases. |
| first_indexed | 2024-12-11T20:42:04Z |
| format | Article |
| id | doaj.art-858a06238f7040b1a189c23a59bd7f2d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T20:42:04Z |
| publishDate | 2012-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-858a06238f7040b1a189c23a59bd7f2d2022-12-22T00:51:28ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-09-012012162,114Nonexistence of asymptotically free solutions to nonlinear Schrodinger systemsNakao HayashiChunhua LiPavel I. NaumkinWe consider the nonlinear Schrodinger systems $$displaylines{ -ipartial _tu_1+frac{1}{2}Delta u_1=F( u_1,u_2), cr ipartial _tu_2+frac{1}{2}Delta u_2=F( u_1,u_2) }$$ in n space dimensions, where F is a p-th order local or nonlocal nonlinearity smooth up to order p, with $1<pleq 1+frac{2}{n}$ for $ngeq 2$ and $1<pleq 2$ for n=1. These systems are related to higher order nonlinear dispersive wave equations. We prove the non existence of asymptotically free solutions in the critical and sub-critical cases.http://ejde.math.txstate.edu/Volumes/2012/162/abstr.htmlDispersive nonlinear wavesasymptotically free solutions |
| spellingShingle | Nakao Hayashi Chunhua Li Pavel I. Naumkin Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems Electronic Journal of Differential Equations Dispersive nonlinear waves asymptotically free solutions |
| title | Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems |
| title_full | Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems |
| title_fullStr | Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems |
| title_full_unstemmed | Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems |
| title_short | Nonexistence of asymptotically free solutions to nonlinear Schrodinger systems |
| title_sort | nonexistence of asymptotically free solutions to nonlinear schrodinger systems |
| topic | Dispersive nonlinear waves asymptotically free solutions |
| url | http://ejde.math.txstate.edu/Volumes/2012/162/abstr.html |
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