Dynamics of Lump-periodic, breather and two-wave solutions with the long wave in shallow water under gravity and 2D nonlinear lattice

Abstract

A lump solution is a rational function solution which is real analytic and decays in all directions of space variables. The equation under consideration in this study is the (2 + 1)-dimensional generalized fifth-order KdV equation which demonstrates long wave movements under the gravity field and in a two-dimensional nonlinear lattice in shallow water. The collisions between lump and other analytic solutions is studied in this work. Using Hirota bilinear approach, lump-periodic, breather and two-wave solutions are successfully reported. In order to shade more light on the characteristics of the acqured solutions, numerical simulations have been performed by means of the 3-dimensional and contour profiles under careful choice of the values of the parameters involved.