Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan–Porsezian–Daniel model by generalized projective Riccati equations method

In this article, the soliton solutions of the nonlinear Lakshmanan–Porsezian–Daniel (LPD) model are extracted, using generalized projective Riccati equations method. The proposed model is discussed for Kerr law, parabolic law and anti-cubic law of nonlinearity. As a result, some new solitary wave solutions are obtained in a unified way. These solitary wave solutions include kink-shaped, bell-shaped, singular solitons and periodic solutions. The constraint conditions for the validity of the constructed solutions are also provided. In order to understand the physical dynamics of the LPD model, some obtained solitons are presented graphically. •The LPD model is investigated using generalized projective Riccati equations method.•The model is solved for Kerr law, parabolic law and anti-cubic law of nonlinearity.•As a result, some solitary wave solutions are obtained in a unified way.•These solutions include kink-shaped, bell-shaped, singular and periodic solitons.