Abstract
In this study, the propagation mechanism of the unstable modulated structures (e.g., rogue wave (RW)) in the framework of the family of a Korteweg–de Vries (KdV) equation is discussed. Using the derivative expansion method, the KdV is converted to a nonlinear Schrödinger equation (NLSE); from now on, we refer to it as the KdV-NLSE. After that we shall discuss whether the KdV-NLSE is suitable for describing the rogue waves (RWs) or not. Also, we shall present some appropriate methods to discuss such waves in the event that the KdV-NLSE fails to describe them.
•The relation between the KdV equation and the NLSE is obtained (KdV-NLSE).•The NLSE for arbitrary wavenumber is derived using the derivative expansion method.•The KdV-NLSE could be used only for describe the stable modulated structures.•The KdV-NLSE cannot support the unstable modulated structures (the RW and breathers).