Abstract
Abstract Researching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation. We have used the sine-Gordon expansion method (SGEM) during this research. We have given the 2D, 3D, and contour graphs acquired from the values of the solutions obtained using strong SGEM.
Highlights
The study of nonlinear differential equation (NLDE) solutions attracts the attention of scientists
We need to explore the solutions of NLDE that have an important place in applied mathematics
Wolfram Mathematica 9 gives the values of .Ai, Bi, μ and c substituting the values of Ai, Bi, μ and c in Eq(10), we can find new analytical solutions to Eq (9)
Summary
The study of nonlinear differential equation (NLDE) solutions attracts the attention of scientists. Esin Inan Eskitasçıoglu et al Applied Mathematics and Nonlinear Sciences 4(2019) 93–100 and improved Bernoulli subequation function method [22], have been successfully considered to find the exact solutions of a wide variety of NLDEs and many others [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88]. Where γ is a real constant with a non-zero value, by using the sine-Gordon expansion method (SGEM)
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