Gauge transformations of constrained KP flows: New integrable hierarchies

Integrable systems in 1+1 dimensions arise from the KP hierarchy as symmetry reductions involving square eigenfunctions. Exploiting the residual gauge freedom in these constraints new integrable systems are derived. They include generalizations of the hierarchy of the Kundu–Eckhaus equation and higher‐order extensions of the Yajima–Oikawa and Melnikov hierarchies. Constrained modified KP flows yield further integrable equations such as the hierarchies of the derivative NLS equation, the Gerdjikov–Ivanov equation, and the Chen–Lee–Liu equation.