Nonlinear Wave Molecules for the Lakshmanan-Porsezian-Daniel Equation in Nonlinear Optics and Biology

The nonlinear wave molecules of the Lakshmanan-Porsezian-Daniel (LPD) equation describing the propagation of ultrashort optical pulses through optical fibers and Davydov soliton in alpha-helical proteins are investigated. Based on the analysis of characteristic lines, the breather molecules consisting of two, three, or even four different breather atoms are derived, and the synthesis modes of molecules by adjusting the values of the phase parameters are generated. The state conversion of the breather molecules is studied and a variety of converted wave molecules are produced. In particular, it is reported that the full conversion of the breather molecules does not exist in the LPD equation. The formation mechanisms of different types of nonlinear wave molecules through the nonlinear superposition are further explored and the influence of higher-order effects on the breather molecules is discussed. Finally, the intricate interactions between the molecules and nonlinear waves are considered. It is found that the distances between atoms in the molecules as well as the shapes of the converted waves change after the interactions, and the essence of such shape-changed interactions is revealed.