Solitary wave solutions for the fourth-order nonlinear Schrödinger equation with variables coefficients

We study the existence and propagation properties of solitary waves within the framework of a fourth-order nonlinear Schrödinger equation with variables coefficients. The model applies to the description of the transport of biological energy inside alpha helical proteins. Both gray, dipole and tripole types are found by adopting the complex multipole ansatz solution. Parametric conditions for the existence of the solitary wave solutions are presented and their dynamic behavior is analyzed for different choice of system parameters. In addition, the stability of the tripole-managed solitons under some initial perturbations is studied by employing the numerical simulation methods. Finally, the collision dynamics of two similar tripole solitons in an inhomogeneous periodic medium is explored.