Dipole solitons in an extended nonlinear Schrödinger's equation with higher-order even and odd terms

We investigate the extended nonlinear Schrödinger equation with higher-order odd and even terms. The model includes additional higher-order dispersion and nonlinear terms that are most important for applications in fiber optics, in the case of the Heisenberg spin chain, and for ocean waves. Special exact solutions in the form of a dipole soliton is obtained, by adopting a complex amplitude ansatz composed of the product of bright and dark solitary waves. The conditions on the system parameters for the existence of this localized structure are also reported. The derived solution characteristically exists due to a balance among physical effects of different nature. Numerical results and discussions are also presented.