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Exact solutions of the time fractional nonlinear Schrödinger equation with two different methods
Author(s) -
Lashkarian Elham,
Hejazi S. Reza
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4770
Subject(s) - mathematics , invariant subspace , homogeneous space , nonlinear system , lie group , invariant (physics) , nonlinear schrödinger equation , fractional calculus , mathematical analysis , schrödinger equation , lie theory , mathematical physics , pure mathematics , linear subspace , adjoint representation of a lie algebra , physics , quantum mechanics , geometry , lie conformal algebra
In the present paper, exact solutions of fractional nonlinear Schrödinger equations have been derived by using two methods: Lie group analysis and invariant subspace method via Riemann‐Liouvill derivative. In the sense of Lie point symmetry analysis method, all of the symmetries of the Schrödinger equations are obtained, and these operators are applied to find corresponding solutions. In one case, we show that Schrödinger equation can be reduced to an equation that is related to the Erdelyi‐Kober functional derivative. The invariant subspace method for constructing exact solutions is presented for considered equations.