Construction of localized coherent structures based on the (3 + 1)-dimensional Nizhnik–Novikov–Veselov equation

Abstract In this study, standard truncated Painleve analysis is used to obtain localized coherent structures based on the (3 + 1)-dimensional Nizhnik–Novikov–Veselov equation. By applying a special Backlund transformation and introducing arbitrary functions of seed solutions, the abundance of localized structures are derived. Furthermore, by selecting the arbitrary functions under the conditions of this study, some special types of localized structures are constructed.