Solvable cubic resonant systems (Q2422486)

The authors have found a new conserved quantity for a class of nonlinear partial differential system of equations which provides resonant and periodic properties. The authors give a rigorous proof of this statement. Analogies can be found in applications of the Gross-Pitaevsky equation and nonlinear wave equations in an Anti-de Sitter spacetime. For further connections with physics, the reviewer recommends the book: [\textit{J. Liu} et al., Nonlinear adiabatic evolution of quantum systems. Geometric phase and virtual magnetic monopole. Singapore: Springer (2018; Zbl 1405.81009)].