Asymptotic analysis of resonance behaviors for the (2+1)-dimensional generalized fifth-order KdV equation via Hirota's bi-linear method

Abstract The generalized fifth-order Korteweg–de Vries (KdV) equation, encompasses certain characteristics of the original KdV equation and is capable of describing more complex wave phenomena. The Miles resonance conditions are achieved for Y -shaped solitons by rendering the phase shift induced by the elastic interaction among N -solitons. Our investigation not only conducts a thorough analysis of the low-order resonant solutions but also presents general resonant conditions that enable the degeneration of N -solitons solutions into resonant solutions.