Exploring the generalized fifth-order (2 + 1)-dimensional KdV equation: The lump structures and collision phenomena to the shallow water under gravity and nonlinear lattice

Abstract

This study deals the lump structures and interaction phenomena to the (2 + 1)-dimensional generalized fifth-order KdV (2GKdV) equation which demonstrates long wave movements under the gravity field and in a two-dimensional nonlinear lattice in shallow water. A variety of solutions like lump periodic, collision between lumps and hyperbolic solutions as well as exponential solutions, breather waves, two wave solutions are under consideration. The Hirota perturbation expansion technique with setting nonzero background wave has been adopted for investing the studied model and securing the solutions. A lump solution is a rational function solution which is real analytic and decays in all directions of space variables. Breather waves refer to solitary waves that exhibit both partial localization and periodic structure in either space or time. Breathers serve crucial functions in nonlinear physics and have been observed in various physical domains, including optics, hydrodynamics, and quantized superfluidity. The specified parameter values produce a variety of graphs with distinctive shapes to visually represent the results. The technique’s performance, clarity, and visibility are highlighted in its suitability for various nonlinear equations in computational physics and other research domains, illustrating collision-related components and solution properties.