A new nonlinear integrable fifth-order equation: multiple soliton solutions with unusual phase shifts

Abstract

In this work, a new nonlinear integrable fifth-order equation has been developed, which is examined to explore the movable critical points by using Painlevé test. It has been demonstrated that this equation passes the Painlevé test along with required number of arbitrary functions to confirm its complete integrability. Also, the newly developed equation is characterized by real and complex dispersion relations. Various types of multiple soliton solutions and multiple complex soliton solutions are furnished uniformly by employing the Hirota’s direct method. The interaction of solitons reveal unusual phase shifts, which are unlike the KdV type of phase shifts.