Eckhaus equation
In mathematical physics, the Eckhaus equation – or the Kundu–Eckhaus equation – is a nonlinear partial differential equations within the nonlinear Schrödinger class:
The equation was independently introduced by Wiktor Eckhaus and by Anjan Kundu to model the propagation of waves in dispersive media. The Kundu–Eckhaus equation admits many different types of analytical solutions – just like the nonlinear Schrödinger equation – including but not limited to rational rogue wave solutions. Behavior of its stochastic rogue wave solutions and their spectra may be used for early detection purposes.Linearization
The Eckhaus equation can be linearized to the linear Schrödinger equation:
through the non-linear transformation:
The inverse transformation is:
This linearization also implies that the Eckhaus equation is integrable.
