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On the rational sine-Gordon solution of the forced KdV equation Cover

On the rational sine-Gordon solution of the forced KdV equation

International Journal of Mathematics and Computer in Engineering
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By: Wei Gao and  Carlo Cattani  
Open Access
|Feb 2026

Figures & Tables

Fig. 1

Parametric nature wave behaviors for equation (18) at (a) : τ(t) = sin(t), (b) : τ(t) = cos(t), (c) : τ(t) = tan(t) and (d) : τ(t) = cot(t).
Parametric nature wave behaviors for equation (18) at (a) : τ(t) = sin(t), (b) : τ(t) = cos(t), (c) : τ(t) = tan(t) and (d) : τ(t) = cot(t).

Fig. 2

Parametric nature wave behaviors for equation (20) at (a) : F(t) = sin(t), (b) : F(t) = cos(t), (c) : F(t) = tan(t) and (d) : F(t) = cot(t), and also τ(t) = cos(t).
Parametric nature wave behaviors for equation (20) at (a) : F(t) = sin(t), (b) : F(t) = cos(t), (c) : F(t) = tan(t) and (d) : F(t) = cot(t), and also τ(t) = cos(t).

Fig. 3

Parametric nature wave behaviors for equation (22) at F(t) = sin(t) cos(t) tan(t) is (a)3D, and (b) Contour, respectively, and also τ = cos(t).
Parametric nature wave behaviors for equation (22) at F(t) = sin(t) cos(t) tan(t) is (a)3D, and (b) Contour, respectively, and also τ = cos(t).

Fig. 4

2D wave behavior for equation (22) at F(t) = sin(t) cos(t) tan(t) with 2D, and t = 8.5, and also τ(t) = cos(t), τ(t) = sin(t), respectively.
2D wave behavior for equation (22) at F(t) = sin(t) cos(t) tan(t) with 2D, and t = 8.5, and also τ(t) = cos(t), τ(t) = sin(t), respectively.

Fig. 5

The wave way behavior for equation (25) at τ(t) = cos(t) with a) 3D and b) Contour.
The wave way behavior for equation (25) at τ(t) = cos(t) with a) 3D and b) Contour.
DOI: https://doi.org/10.2478/ijmce-2026-0001 | Journal eISSN: 2956-7068
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Language: English
Submitted on: Nov 8, 2024
|
Accepted on: Dec 2, 2024
|
Published on: Feb 2, 2026
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
KdV equation with forcing term,
analytical method,
travelling waves,
wave ways,
solitary nature of the waves
Related subjects:
Computer sciences,
Computer sciences, other,
Engineering,
Introductions and overviews,
Engineering, other,
Mathematics,
General mathematics,
Physics,
Physics, other

© 2026 Wei Gao, Carlo Cattani, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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