Rogon-like solutions excited in the two-dimensional nonlocal nonlinear Schrödinger equation

We report the analytical one- and two-rogon-like solutions for the two-dimensional nonlocal nonlinear Schrödinger equation by means of the similarity transformation. These obtained solutions can be used to describe the possible physical mechanisms for rogue-like wave phenomenon. Moreover, the free function of space y involved in the obtained solutions excites the abundant structures of rogue-like wave propagations. The Hermite-Gaussian function of space y (normalized function) is, in particular, chosen to depict the dynamical behaviors for rogue-like wave phenomenon.