Intricate dynamics of rogue waves governed by the Sasa–Satsuma equation

We present the second order rogue wave solutions of the Sasa–Satsuma evolution equation that have significantly more complicated structure than in the case of the nonlinear Schrödinger equation. This equation takes into account the third order dispersion, self-frequency shift and self-steepening effects, thus making it closer to realistic physical applications. These effects are important both for water waves and pulses in optical fibres. Although the Sasa–Satsuma equation is integrable, the degree of complexity of these new solutions has prevented them being found previously. Here, we present in explicit form the second-order rogue wave solutions of the Sasa–Satsuma equation for three free parameter values of the family of rogue wave solutions. Special choices of the free parameters allow us to present these solutions in the simplest possible way and to illustrate them graphically.