Higher-order semirational solutions and W-shaped solitons for the multi-component AB system

Abstract

The multi-component AB system, which appears in the ultra-short optical pulse field and the geophysical fluid dynamics, is investigated via the Darboux transformation technique. Combining the special vector solutions for the Lax pair and the corresponding Darboux transformation, the higher-order semirational solutions for the AB system are constructed. Besides, the semirational solutions are discussed in three different types: (1) the degenerate case that higher-order rogue waves (RWs); (2) higher-order RWs coexisting with multi bright and dark solitons; (3) higher-order RWs coexisting with multi breathers. Through studying the modulation instability analysis for the AB system, some higher-order W-shaped solitons are constructed when the modulation instability growth rate becomes zero. It is interesting that the first- and second-order W-shaped solitons in the last components q, r and s are the plane waves, and the normal W-shaped solitons exist in not less than third order case.