Abstract
This research paper employs two different computational schemes to the couple Boiti–Leon–Pempinelli system and the (3+1)-dimensional Kadomtsev–Petviashvili equation to find novel explicit wave solutions for these models. Both models depict a generalized form of the dispersive long wave equation. The complex, exponential, hyperbolic, and trigonometric function solutions are some of the obtained solutions by using the modified Khater method and the Jacobi elliptical function method. Moreover, their stability properties are also analyzed, and for more interpretation of the physical features of the obtained solutions, some sketches are plotted. Additionally, the novelty of our paper is explained by displaying the similarity and difference between the obtained solutions and those obtained in a different research paper. The performance of both methods is tested to show their ability to be applied to several nonlinear evolution equations.
Highlights
A water wave is a basic example of the dispersive long waves that propagate on the water surface with surface tension and gravity
The linear dispersion relation was first discovered by Pierre– Simon Laplace and the linear water wave theory was derived by George Biddell Airy in 1840.9–14 Benjamin–Bona–Mahony equation, Camassa–Holm equation, Davey–Stewartson equation, Kadomtsev– Petviashvili (KP) equation, Korteweg–de Vries equation, nonlinear Schrödinger equation, shallow water equations, and couple Boiti– Leon–Pempinelli (BLP) system are considered as the foundational models of the dispersive water-wave models
This section studies the novelty of our presented paper by making a comparison between our solutions and those obtained in previous research paper
Summary
Dispersion usually refers to the frequency dispersion in fluid dynamics, which explains the different phase speeds of the traveling waves with different wavelengths. A water wave is a basic example of the dispersive long waves that propagate on the water surface with surface tension and gravity. the dispersive medium is generally referred to as the water with a free surface. Calculating the value of the balance between the highest order derivative term and the nonlinear term in Eq (5), leads to N = 1. All of these properties and abilities of the nonlinear partial differential equations are used to describe the natural phenomena. According to these properties, many mathematicians developed some methods and still trying to find new general methods to get exact and solitary traveling wave solutions of these models.
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