Heavy sea states and severe weather conditions have caused the loss of more than 200 super carriers within the last 20 years. In many cases single 'rogue waves' of abnormal height as well as groups of extreme waves have been reported by crew members of such vessels. The European Project MAXWAVE deals with both theoretical aspects of extreme waves as well as new techniques to observe these waves...

Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing unidirectional propagation shallow-water waves and perform Painlev\'e analysis to understand its integrability nature. We construct explicit form higher-order rogue wave solutions by adopting Hirota's bilinearization polynomia...