Dipole soliton solution for the homogeneous high-order nonlinear Schrödinger equation with cubic-quintic-septic non-Kerr terms

We consider a high-order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic-quintic-septic nonlinearities, self-steepening, and instantaneous Raman response. This equation models describes ultra-short optical pulse propagation in highly-nonlinear media. The ansatz solution of Choudhuri and Porsezian (in Ref. [16]) is adapted to investigate solutions composed of the product of bright and dark solitary waves. Parametric conditions for the existence of the derived soliton solutions are given and their stabilities are numerically discussed. These exact solutions provide insight into balance mechanisms between several high-order nonlinearities of different nature.