Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

Abstract

The study of nonlinear evolution equations is a subject of active interest in different fields including physics, chemistry, and engineering. The exact solutions to nonlinear evolution equations provide insightful details and physical descriptions into many problems of interest that govern the real world. The Kadomtsev–Petviashvili (kp) equation, which has been widely used as a model to describe the nonlinear wave and the dynamics of soliton in the field of plasma physics and fluid dynamics, is discussed in this article in order to obtain solitary solutions and explore their physical properties. We obtain several new optical traveling wave solutions in the form of trigonometric, hyperbolic, and rational functions using two separate direct methods: the (w/g)-expansion approach and the Addendum to Kudryashov method (akm). The nonlinear partial differential equation (nlpde) is reduced into an ordinary differential equation (ode) via a wave transformation. The derived optical solutions are graphically illustrated using Maple 15 software for specific parameter values. The traveling wave solutions discovered in this work can be viewed as an example of solutions that can empower us with great flexibility in the systematic analysis and explanation of complex phenomena that arise in a variety of problems, including protein chemistry, fluid mechanics, plasma physics, optical fibers, and shallow water wave propagation.

Simulation of a Combined (2+1)-Dimensional Potential Kadomtsev–Petviashvili Equation via Two Different Methods

“…Here, R(ξ) represents Equation (7). Considering this, Equation ( 11) will be substituted into Equation (9).…”

“…The examination of solutions of these equations has become crucial across various fields of science and technology, including control theory, fiber optics, solid-state mechanics, transport infrastructure, atomic engineering, fluid dynamics, and various other research fields. Numerous successful approaches have been devised for investigating dynamic structures, such as lump solutions [1,2], the matrix eigenvalue problem [3], auto-Backlund transformations [4], the auxiliary equation method [5], the generalized Riccati equation mapping technique [6], the addendum to the Kudryashov technique [7], the unified method [8], the modified extended tanh-function approach [9], the Hirota bilinear technique [10], the Lie symmetry approach [11], the improved Bernoulli sub-equation function procedure [12], the modified (G ′ /G)-expansion method [13], the bilinear method [14], an extended (G ′ /G)-expansion method [15], the tanh-coth method [16,17], and so on.…”

Dynamic Properties of Non-Autonomous Femtosecond Waves Modeled by the Generalized Derivative NLSE with Variable Coefficients

“…Studies on optical wave solutions through optical fiber media that demonstrate quintic nonlinearity and self-steepening influence have become vigorous, continuous and are motivated by their important applications, owing to their ability of propagating long distances without wane and due to their various geometrical structures, to high-capacity fiber telecommunications, and to all optical switches [1][2][3][4][5]. In many aspects of mathematics and science, including nonlinear optics, hydrodynamics, quantum physics, nonlinear acoustics, and many others, the nonlinear Schrödinger equation (NLSE) and its relatives have an essential role in this aspect [6][7][8][9][10][11][12].…”