| Title | GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE FOURTH ORDER ̈ NONLINEAR SCHR ODINGER TYPE EQUATION |
| Publication Type | Journal Article |
| Year of Publication | 2007 |
| Authors | Segata, J-ichi, Shimomura, A |
| Secondary Title | Communications in Applied Analysis |
| Volume | 11 |
| Issue | 2 |
| Start Page | 169 |
| Pagination | 188 |
| Date Published | 04/2007 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 35B40, 35Q55 |
| Abstract | We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrodinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.
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| URL | http://www.acadsol.eu/en/articles/11/2/3.pdf |
| Short Title | Global Existence and Asymptotic Behavior |
| Refereed Designation | Refereed |
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