Painlevé analysis and higher-order rogue waves of a generalized (3+1)-dimensional shallow water wave equation

Abstract

Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform Painlevé analysis to understand its integrability nature. We construct the explicit form of higher-order rogue wave solutions by adopting Hirota’s bilinearization and generalized polynomial functions. Further, we explore their dynamics in detail, depicting different pattern formation that reveal potential advantages with available arbitrary constants in their manipulation mechanism. Particularly, we demonstrate the existence of singly-localized line-rogue waves and doubly-localized rogue waves with multiple (single, triple, and sextuple) structures generating triangular and pentagon type geometrical patterns with controllable orientations that can be altered appropriately by tuning the parameters. The presented analysis will be an essential inclusion in the context of rogue waves in higher-dimensional systems.

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

“…Rogue waves with short periods, large amplitudes, and extremely destructive waves have been studied frequently in the latest research of oceanography and physics. Rogue waves are unexpected large water waves that appear and disappear suddenly, with extremely steep peaks, and even pose a great threat to large ships [1][2][3][4][5][6][7]. Interaction solutions can be used to explain nonlinear phenomena, especially in climate modeling and prediction, weather forecasting, fluid dynamics, geophysics, etc Many scholars did a lot of work on the interaction phenomena and obtained many meaningful interaction solutions [8][9][10][11][12][13][14][15].…”

General high-order lump solutions and their dynamics in the Levi equations

“…By these methods many different types of exact solutions are obtained, such as soliton solutions [22][23][24], periodic solutions [25,26], rational solutions [27][28][29][30] and hybrid solutions [31,32], etc. Because of their physical importance, rogue waves, also known as monster waves, freak waves, or killer waves, have been studied intensively in theory and experiment over the past few decades [33][34][35][36][37][38]. Rogue wave solutions are rational functions in terms of both space and time.…”

Localized waves and interaction solutions to an integrable variable coefficients Jimbo-Miwa equation

“…In the following we will use Painlevé analysis to check the integrability of equation (1.5) [45][46][47][48]. With the help of symbolic computation, resonances occur at r = − 1, 1, 4, and 6, where r = − 1 corresponds to the arbitrariness of the singular manifold.…”