Rogue waves of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

摘要

General high-order rogue waves of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation are derived by employing the bilinear method. These rogue wave solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that fundamental rogue waves in the (x, z) plane are line rogue waves, which arise from the constant background with a line profile and then disappear into the constant background again. The typical dynamics in other planes have also been illustrated by three dimensional plots. It is also shown that high-order rogue waves in the (x, z) plane are parallel line rogue waves, which also arise from the constant background and then decay back to it. Besides, dynamical behaviours of these high-order rogue waves in the (x, y) and (x, t) planes are also illustrated.