Spatial Self-Similar Transformation and Novel Line Rogue Wave of the Fokas System

Fokas system is a natural and simple extension of the (2+1)-dimensional Schrödinger equation which can be used to describe optical pulse propagation in the nonlocal optical fibers. We first propose a two-dimensional spatial self-similar transformation of the Fokas system which is translated into the (1+1)-dimensional nonlinear Schrödinger equation. And then construct its abundant line rogue waves excitation. It is found that the spatial coherent structure line rogue waves induced by the Akhmediev breathers and Kuznetsov-Ma solitons also have the short life characteristics which possessed for the line rogue waves induced by the Peregrine solitons and other higher-order rogue waves and multi-rogue waves of the (1+1) dimensional standard NLS equations. This is completely different from the evolution characteristics of line soliton structures induced by bright solitons and the multi-solitons, which keeping their shape and amplitude unchanged. The diagram shows the evolution characteristics of the resulting all kinds of line rogue waves. The new excitation mechanism of line rogue waves revealed contributes to the new understanding of the coherent structure of high-dimensional nonlinear wave models.