Infinite hierarchy of nonlinear Schrodinger equations and their solutions

We study the infinite integrable nonlinear Schrodinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that even-order equations in the set affect phase and stretching factors in the solutions, while odd-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.