Abstract
Several novel rational solutions with nonzero boundary condition for the Kundu equation, which is an important physical model, are derived using the technique of generalized Darboux transformation. It is the first time that a systemic analysis has been conducted on such rational solutions for the Kundu equation. For the 1-order rational solutions with nonzero boundary conditions, our findings reveal that three parameters, a, b, and β, which are associated with the effects of self-steepening, self-phase modulation, and quintic nonlinearity in the Kundu equation, can result in four distinct states for case B and five distinct states for case C, all corresponding to rational solutions with nonzero boundary conditions.
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