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Lie symmetries of a generalised non-linear Schrodinger equation. II. Exact solutions
| Content Provider | Scilit |
|---|---|
| Author | Gagnon, L. Winternitz, P. |
| Copyright Year | 1989 |
| Description | Journal: Journal of Physics A: General Physics For pt.I see ibid., vol.21, p.1493 (1988). The authors obtain group-invariant solutions of the non-linear equation i psi$ _{t}$+ Delta psi $=a_{0}$ psi $+a_{1}$ psi mod psi mod$ $^{2}$+a_{2}$ psi mod psi mod$ ^{4}$ for which the symmetry group was previously shown to be the extended Galilei group for $a_{1}a_{2}$ not=0 and the extended Galilei-similitude group for $a_{1}$=0 or $a_{2}$=0. They use the symmetry subgroups to reduce the equation to ordinary differential equations which are solved, whenever possible, with the help of a singularity analysis. Solutions are obtained in terms of elementary functions, Jacobi elliptic functions and Painleve transcendents. |
| Related Links | http://iopscience.iop.org/article/10.1088/0305-4470/22/5/013/pdf |
| Ending Page | 497 |
| Page Count | 29 |
| Starting Page | 469 |
| ISSN | 00223689 |
| DOI | 10.1088/0305-4470/22/5/013 |
| Journal | Journal of Physics A: General Physics |
| Issue Number | 5 |
| Volume Number | 22 |
| Language | English |
| Publisher | IOP Publishing |
| Publisher Date | 1989-03-07 |
| Access Restriction | Open |
| Subject Keyword | Journal: Journal of Physics A: General Physics Ordinary Differential Equation Exact Solution Linear Equations Symmetry Group Elementary Functions Jacobi Elliptic Functions |
| Content Type | Text |
| Resource Type | Article |
