High-order rational solutions and rogue wave for the (2 + 1)-dimensional nonlinear Schrödinger equation

Abstract

In this paper, some exact explicit rational solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation are presented in terms of the Gram determinants by using the bilinear method. The expressions of the fundamental line rogue wave, second-order parallel line rogue wave and third-order parallel line rogue wave all involve determinants whose matrix elements are simple polynomials. These line rogue waves, which all generate from a constant background with line contours and then disappear into the same background, are plotted in the (x, y)-plane. Moreover, we also consider different structures of higher-order rogue waves, and their dynamical behaviors are illustrated in the (x, t)-plane.