New exact solutions for solving the initial-value-problem of the KdV–KP equation via the Lie group method

Abd‐el‐Malek, Mina B.; Amin, Amr M.

doi:10.1016/j.amc.2015.03.117

Cited by 6 publications

(1 citation statement)

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“…Hence, familiarity with all classic and recently established approaches for addressing these models becomes increasingly vital. Over the past few years, numerous strategies have been proposed by mathematicians and scientists, such as the F-expansion method [8], the variational iteration method [9], method of sine-cosine [10], the tanh-function technique [11], the auxiliary equation method [12], the exp-function technique [13,14], the exact soliton solution [15][16][17], the generalized Kudryashov approach [18], and the newly extended generalized Kudryashov approach [19]. A more detailed discussion on some recent direct methods can be found in several related works (see, for example, [20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

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

Alotaibi

2022

Crystals

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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.

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