This paper is devoted to the study of ninth order boundary value problems that emerge in the mathematical modeling of AFTI-F16 fighter. An augmented longitudinal and lateral dynamics of the AFTI-F16 fighter is described by ninth order differential equations, containing unknown parameters which can be determined using automated system identification algorithms. The solution of the boundary value problem is obtained in terms of a convergent series using homotopy analysis method (HAM). The method is effectively applied on numerical examples and the results are compared with those given in the literature, revealing that the presented method gives better approximations to the exact solution.
The prime goal of this study is to investigate novel solutions of two well-known nonlinear models namely the $$(2+1)$$
(
2
+
1
)
-dimensional Zoomeron equation and the foam drainage equation by utilizing a powerful technique; the extended $$\left(\frac{G'}{G^{2}}\right)$$
G
′
G
2
-expansion method. Using this methodology, the hyperbolic function solutions, the trigonometric function solutions and the rational function solutions are constructed. Abundant soliton solutions are retrieved from the obtained results. The dynamical structures of the solutions are illustrated graphically through 3-dimensional graphs and the corresponding contour plots. The reported results depict the effectiveness and capability of the extended $$\left(\frac{G'}{G^{2}}\right)$$
G
′
G
2
-expansion method for handling different nonlinear partial differential equations.
The modified auxiliary equation (MAE) approach and the generalized
projective Riccati equation (GPRE) method are used to solve the Zoomeron
problem in this study. Different types of exact traveling wave solutions
are achieved, including solitary wave, periodic wave, bright, dark
peakon, and kink-type wave solutions. Earned results are given as
hyperbolic and trigonometric functions. Moreover, the dynamical features
of obtained results are demonstrated through interesting plots.
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