Dynamics of N th-order rogue waves in ( $$2+1$$ 2 + 1 )-dimensional Hirota equation

Abstract

Inspired by the works of Ohta and Yang, we construct general high-order rogue wave solutions for the \((2+1)\) -dimensional Hirota equation using the bilinear transformation method. The formula of the solutions can be represented in terms of determinants. It is shown that the order of rogue waves will depend on the roots of determinants. These rogue waves are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. In addition, some interesting dynamic patterns of rogue waves are exhibited in the (x, y) and (x, t) planes.

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