Abstract
The current study is dedicated to find the complex soliton solutions of the hyperbolic (2+1)-dimensional nonlinear Schrödinger equation. In this direction we takes the help of Lie Symmetry analysis method. First of all we obtained the invariant condition which play important role in the mechanism of Lie symmetry method. After that we obtained the symmetries of the hyperbolic Schrödinger equation. These symmetries are further used to develop the appropriate vector fields. Consequently, with the application of these vector field optimal system of subalgebras are obtained. Further, under the each subalgebras similarity solutions are obtained in form of trigonometric functions. Most important the similarity variables which are obtained with the help of Lie symmetry method are in form of hyperbolic function. This clearly indicate that the phenomenon modeled by the hyperbolic Schrödinger equation invariant under these similarity solutions and similarity variable. At the end of the study complex soliton are obtained for Schrödinger equation which are in form of trigonometric and hyperbolic functions.
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