Abstract
Pseudopotential of Ablowitz–Ladik equation is proposed for the first time, form which a new Darboux–Bäcklund transformation is established. Various type of nonlinear localized wave solutions including rogue, period, n- and t-direction breather wave solution are derived by choosing suitable eigenvalue problems, and the corresponding dynamical properties and evolutions are illustrated. Besides, the corresponding matching relations to solutions of the Nonlinear Schrödinger equation are also defined. The obtained nonlinear wave solutions may raise the possibility of related experiments and potential applications in nonlinear optics and other fields of nonlinear science, such as Bose–Einstein condensates and ocean waves.
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