Representing rogue waves in minimal form

Nonlinearity can cause rogue waves to appear on ocean surfaces, as pulses in fibers and in other systems. We investigate how to describe these rogue waves using minimal order polynomials. The method here gives the lowest order polynomial description of the nonlinear Schrödinger equation rogue wave of order n. In fact, while polynomials up to order n(n+1) are needed to write the solutions directly, here we only require polynomials of one half of this order. We then use these forms to readily determine useful integral invariants.