On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models

doi:10.1016/S0034-4877(00)89037-0

Reports on Mathematical Physics

Volume 45, Issue 2, April 2000, Pages 273-291

https://doi.org/10.1016/S0034-4877(00)89037-0 Get rights and content

Abstract

We perform classification of a class of one-dimensional nonlinear Schrödinger equations whose symmetry groups have dimensions n = 1, 2, 3. Next, from so constructed classes of invariant equations we select those nonlinear Schrödinger equations which are invariant with respect to the Galilei group and its natural extensions. The results obtained are applied for the symmetry classification of complex Galilei-invariant Doebner-Goldin models.

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^∗: Permanant address: Institute of Mathematics of the Academy of Sciences of Ukraine, Tereshchenkivska Street 3, 252004 Kyiv, Ukraine.

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On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models

Abstract

Phys. Lett. A

Phys. Lett. A

Phys. Lett. A.

Phys. Lett. A

Ann. Phys.

J. Phys. A: Math. Gen.

Commun. Math. Phys.

Lett. Nuovo Cim.

Inverse Problems

Rep. Math. Phys.

J. Phys. A: Math. Gen.

Group Analysis of Differential Equations