Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-02-18
J. Math. Phys., (2011), 52, 093702
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
Analytical solutions of variable coefficient nonlinear Schr\"odinger equations having four-dimensional symmetry groups which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional are obtained using two different tools. The first tool is to use one dimensional subgroups of the full symmetry group to generate solutions from those of the reduced ODEs (Ordinary Differential Equations), namely group invariant solutions. The other is by truncation in their Painlev\'e expansions.
Gungor Faruk
Ozemir Cihangir
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