Higher-order rogue waves and exotic dynamic patterns in the three-component local and nonlocal Gross-Pitaevskii equations

Abstract

In this work, higher-order rogue wave solutions in the three-component local and nonlocal Gross-Pitaevskii equations are investigated. The first-order rogue wave solution for the three-component local and nonlocal Gross-Pitaevskii equations is derived using the Darboux transformation combined with a variable separation technique. In order to efficiently construct higher-order rogue wave solutions for the three-component local and nonlocal Gross-Pitaevskii equations, we establish a relationship between the three-component and the one-component versions of the nonlinear Schrödinger equation. Then using this relationship, we obtain the higher-order rational solutions for the three-component local and nonlocal Gross-Pitaevskii equations, which describe the rogue wave patterns. Moreover, the main characteristics of these rogue waves are graphically examined by varying the free parameters. In particular, these results show that rogue waves in the three-component nonlocal Gross-Pitaevskii equations may exhibit a much richer variety than those in the corresponding local equations.