Rogue Waves for the Coupled Schrödinger–Boussinesq Equation and the Coupled Higgs Equation

In this work, firstly it is shown that the coupled Schrodinger–Boussinesq equation, which governs the nonlinear propagation of coupled Langmuir and dust-acoustec wave in a multicomponent dusty plasma, possesses rogue waves in the form of the rational solutions. Here a hierarchy of rational solutions, the Peregrine breather and the second-order rational solution are given by means of the Hirota technique. Also, it is worth noting that the electric field exhibits bright rogue wave feature while electrostatic potential plays a role of dark rogue wave. Meanwhile, in comparison with rogue wave of nonlinear Schrodinger equation, some novel features of rogue waves are presented in their second order rational solutions. Secondly, rational solution of the coupled Higgs equation is taken into account by utilizing Hirota technique and the existence condition of rogue wave for this system is discussed.

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