Talbot carpets by rogue waves of extended nonlinear Schrödinger equations

We present analytical and numerical double-periodic solutions of the one-dimensional nonlinear Schrödinger equation and its extended versions in the form of Talbot carpets. The breathers and rogue waves of different orders are obtained using numerical simulations, starting from the initial conditions calculated by the Darboux transformation. To suppress undesirable aspects of modulation instability leading to homoclinic chaos, Fourier mode pruning procedures are invented to preserve and maintain the twofold periodicity of carpets. The novelty of this paper is analytical Talbot carpets for Hirota–quintic equation and ability to obtain them dynamically by controlling the growth of the Fourier modes. In addition, the new period-matching procedure is also described for periodic rogue waves that can be utilized to produce Talbot carpets without mode pruning. Tablot carpets may find future utility in optoplasmonic nanolithography.