The breather solutions and propagation features analysis for Lakshmanan–Porsezian–Daniel equation

The breather solutions for Lakshmanan-Porsezian-Daniel equation with fourth-order dispersion and fifth-order nonlinearity are studied in this paper. The breather solutions under plane wave background are solved by bilinear method and different evolution situations under different parameters are analyzed. Based on cascading instabilities analysis for the first several Fourier modes, the times at which the first breather occurs are predicted on about the same order of magnitude. By numerical simulations, multiple breathers recurrence after the first breather is formed in time can be observed, that is the Fermi-Pasta-Ulam-Tsingou recurrence phenomena appears. The effects of the higher-order coefficient and the plane wave background parameter on the propagation of the breather waves and the chaotic behavior of the Fourier mode are also discussed.