Dynamics of general higher-order rogue waves in the two-component long wave–short wave model of Newell type

Abstract

An integrable two component long-wave–short-wave (2-LS) model of Newell type governing the resonant interaction between two capillary waves with a common gravity wave is considered. The general higher order rogue wave (RW) solutions of this system are obtained by employing the bilinear KP hierarchy reduction method. Our study explores three different families of RWs depending upon the root structure of an algebraic equation characterizing them. Those are the Nth-order bounded rogue waves, mixed bounded (N1,N2)th-order rogue waves and degradable bounded (N¯1,N¯2)th-order rogue waves, respectively, where N,N1,N2 are arbitrary positive integer and N¯1,N¯2 are arbitrary non-negative integers. It is interesting to note that the fundamental rogue wave in one short wave (SW) component can attain a peak amplitude as high as more than six times the background amplitude while it is three times the background amplitude in the other SW component. We identify that the Nth-order bounded rogue waves are composed of N(N+1)2 fundamental rogue waves, the mixed bounded (N1,N2)th-order rogue waves comprise N1th-order bounded rogue waves mixing with another type N2th-order bounded rogue waves existing in different state, and the degradable bounded (N¯1,N¯2)th-order rogue waves consist of N¯12+N¯22−N¯1(N¯2−1) fundamental rogue waves. Non-trivial super rouge waves are reported.