Comprehensive analysis of three seventh-order KdV-type equations

Hedli, Riadh; Berrimi, Fella

doi:10.22034/cmde.2025.66573.3121

Comprehensive analysis of three seventh-order KdV-type equations

Document Type : Research Paper

Authors

Riadh Hedli ¹
Fella Berrimi ²

¹ LMFN Laboratory, Mathematics Department, Ferhat Abbas university-Setif 1, Algeria.

² LRSD Laboratory, Computer Science Department, Ferhat Abbas university-Setif 1, Algeria.

10.22034/cmde.2025.66573.3121

Abstract

In this paper, we employ the generalized $\exp(-\psi({\xi}))$-expansion approach to derive analytical solutions for three specific cases of the generalized seventh-order KdV equation: the seventh-order Sawada-Kotera-Ito equation, the seventh-order Lax equation, and the seventh-order Kaup-Kupershmidt equation. These equations hold significant importance in the nonlinear sciences. By utilizing this approach, we obtain a variety of new exact traveling wave solutions for the aforementioned nonlinear models. Moreover, we showcase 2D and 3D contour plots and density plots to acquire comprehensive representations, using cutting-edge scientific instruments. Our results confirm the effectiveness and practicality of the proposed method in solving the aforementioned problems, as well as other nonlinear evolution equations encountered in the domains of engineering and mathematical physics.

Keywords

References

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