Rogue waves of the Nizhnik-Novikov-Veselov equation via self-mapping transformation

This paper introduces a new two-dimensional self-mapping transformation applied to the Nizhnik-Novikov-Veselov equation, resulting in the generation of numerous rogue wave solutions. We discover that temporal-localized and spatiotemporal-localized two-dimensional rogue waves respectively. Notably, these rogue waves emerge from a zero background and subsequently exhibit both algebraic and exponential decay patterns. The proposed technique offers a potential tool for constructing rogue-like waves within (2+1)-dimensional nonlinear wave frameworks. The findings presented here serve as a robust mathematical foundation for advancing both theoretical understanding and practical applications of rogue waves.