Interaction of multiple superposition solutions for the (4+1)-dimensional Boiti-LeonManna-Pempinelli equation

• Published in: Nonlinear dynamics Vol. 105; no. 1; pp. 717 - 734
• Main Authors: Han, Peng-Fei, Bao, Taogetusang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2021; Springer Nature B.V
• Subjects: Aerodynamics; Automotive Engineering; Classical Mechanics; Coefficients; Computational fluid dynamics; Computer simulation; Control; Dynamical Systems; Engineering; Existence theorems; Fluid flow; Hyperbolic functions; Incompressible flow; Incompressible fluids; Mechanical Engineering; Nonlinear phenomena; Original Paper; Physical properties; Vibration; Water waves; Different types of N-soliton solutions; Superposition behavior of different functions; Lump N-soliton solutions and their interaction solutions; (; The Hirota bilinear method; dimensional BLMP equation; Homoclinic test method
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06603-z

Water wave is one of the most common phenomena in nature, and its involves mathematical modeling, aerodynamics, computer simulation, mechanical manufacturing, marine science and so on. Hence, the water wave dynamics of a ( 4 + 1 )-dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid is investigated based on the Hirota bilinear method and homoclinic test method. We are aimed at constructing variable coefficient solutions to the equation under consideration. An existence theorem and corollary about superposition solutions of this equation are proved. The water wave dynamic behaviors of the reported results are presented by a careful choice of the arguments for the trigonometric and hyperbolic functions as the values of the variable coefficients. With the help of Mathematica, the effect of the variable coefficients on the reported results can be clearly seen by the three-dimensional profiles. Compared with the published studied, some completely new mathematical results and physical phenomena are presented in this paper. The results are beneficial to the study of water waves in fluid dynamics, and this technique has opened a new way to explain the physical properties of nonlinear phenomena.