Abstract
In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This equation is integrable and admits Lax pair. The LPD equation is the generalization of the nonlinear Schrodinger (NLS) equation and described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using the sine-cosine method and the hyperbolic tangent method a variety of new exact solutions are obtained. These methods are effective tools for searching exact solutions of nonlinear partial differential equations in mathematical physics. The obtained solutions are found to be important for the explanation of some practical physical problems.
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