Extended nonlinear Schroeodinger equation with higher-order odd and even terms and its rogue wave solutions

We consider an extended nonlinear Schroeodinger equation with higher-order odd (third order) and
even (fourth order) terms with variable coecients. The resulting equation has soliton solutions
and approximate rogue wave solutions. We present these solutions up to second order. Moreover,
specic constraints on the parameters of higher-order terms provide integrability of the resulting
equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota, and
Lakshmanan - Porsezian - Daniel (LPD) equations. The resulting integrable equation admits exact
rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue
waves solutions of the corresponding equations.