title: Infinite hierarchy of nonlinear Schrödinger equations and their solutions.
abstract: We study the infinite integrable nonlinear Schrödinger 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.
authors: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors: A
authors: A
authors: Ankiewicz
authors: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors: D J
authors: DJ
authors: Kedziora
authors: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors: A
authors: A
authors: Chowdury
authors: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
authors: U
authors: U
authors: Bandelow
authors: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors: N
authors: N
authors: Akhmediev