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

• Published in: Communications in nonlinear science & numerical simulation 2021-08, Vol.99, p.105846, Article 105846
• Main Authors: Yusuf, Abdullahi, Sulaiman, Tukur Abdulkadir
• Format: Article
• Language: English
• Subjects: Collision phenomena; Exact solutions; Fifth-order KdV; Gravitational fields; Hirota bilinear; Lattice theory; Nonlinear equations; Nonlinear systems; Numerical analysis; Rational functions; Shallow water
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2021.105846

•A nonlinear model arising in a long wave movements under the gravity field and in a two-dimensional nonlinear lattice in shallow water is investigated.•Novel lump collision phenomena are presented.•Numerical simulation of the reported results is performed. 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.