Elliptic-rogue waves and modulational instability in nonlinear soliton equations

We systematically report higher-order elliptic-rogue wave solutions for integrable nonlinear soliton equations, utilizing a method combining Darboux-B\"acklund transformation with theta functions. By developing this method in conjunction with the modified squared wave function method, a quantitative correspondence between elliptic-rogue waves and the modulational instability is provided, revealing the exciting conditions of elliptic-rogue waves. This approach can also be widely utilized to construct elliptic-rogue waves and investigate modulational stability for other integrable equations.Comment: 22page,3 figure