Lie symmetries of a generalised non-linear Schrodinger equation. II. Exact solutions
- 7 March 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (5) , 469-497
- https://doi.org/10.1088/0305-4470/22/5/013
Abstract
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 =a0 psi +a1 psi mod psi mod 2+a2 psi mod psi mod 4 for which the symmetry group was previously shown to be the extended Galilei group for a1a2 not=0 and the extended Galilei-similitude group for a1=0 or a2=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.Keywords
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