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

Gao, Wei; Cattani, Carlo

doi:10.2478/ijmce-2026-0001

Abstract

The KdV equation with a forcing term is solved by searching the sine-Gordon solution. The KdV equation is converted into a nonlinear ordinary differential equation (NODE). The analytical solutions of the model studied is obtained in terms of some suitable periodic functions. The physical meanings of the parametric dependence of solutions is also studied.

References

Russell J.S., Report on Waves: Made to the Meetings of the British Association in 1842–43, 1845.
Search in Google Scholar Back to article
Korteweg D.J., Vries G.D., On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Philosophical Magazine, 39(240), 422–443, 1895.
Search in Google Scholar Back to article
Tappert F.D., Reminiscences on Optical Soliton Research with Akira Hasegawa, 1998. http://binturong.us/tappert/fred/reminiscences_on_optical_soliton_research.pdf, Accessed: November 07, 2024.
Search in Google Scholar Back to article
Eilbeck C., Solitons Home Page, Department of Mathematics, Heriot-Watt University, 2008. http://www.ma.hw.ac.uk/solitons/, Accessed: November 07, 2024.
Search in Google Scholar Back to article
Tang D.Y., Zhang H., Zhao L.M., Wu X., Observation of high-order polarization-locked vector solitons in a fiber laser, Physical Review Letters, 101(15), 153904, 2008.
Search in Google Scholar Back to article
Causanilles F.S.V., Baskonus H.M., Guirao J.L.G., Bermúdez G.R., Some important points of the Josephson effect via two superconductors in complex bases, Mathematics, 10(15), 2591, 2022.
Search in Google Scholar Back to article
Areshi M., Seadawy A.R., Ali A., AlJohani A.F., Alharbi W., Alharbi A.F., Construction of solitary wave solutions to the (3+1)-dimensional nonlinear extended and modified Quantum Zakharov-Kuznetsov equations arising in quantum plasma physics, Symmetry, 15(1), 248, 2023.
Search in Google Scholar Back to article
Hirota R., Soliton (Chapter 5: Direct methods in soliton theory), Springer, USA, 1980.
Search in Google Scholar Back to article
Fordy A.P., Soliton Theory: A Survey of Results, Manchester University Press, USA, 1990.
Search in Google Scholar Back to article
Wang X.D., Zhu G.Y., Wang L., Exact analytical solutions for moving boundary problems of one-dimensional flow in semi-infinite porous media with consideration of threshold pressure gradient, Journal of Hydrodynamics Ser. B, 27(4), 542–547, 2015.
Search in Google Scholar Back to article
Cherniha R., New Q-conditional symmetries and exact solutions of some reaction-diffusion-convection equations arising in mathematical biology, Journal of Mathematical Analysis and Applications, 326(2), 783–799, 2007.
Search in Google Scholar Back to article
Gasmi B., Ciancio A., Moussa A., Alhakim L., Mati Y., New analytical solutions and modulation instability analysis for the nonlinear (1+1)-dimensional Phi-four model, International Journal of Mathematics and Computer in Engineering, 1(1), 79–90, 2023.
Search in Google Scholar Back to article
Wang J., Wang Q., Dai H.H., Stress-free bending of a neo-Hookean plate induced by growth: Exact solution and experiments, International Journal of Non-Linear Mechanics, 106, 280–287, 2018.
Search in Google Scholar Back to article
Usman M., Hussain A., Ali H., Zaman F., Abbas N., Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons, International Journal of Mathematics and Computer in Engineering, 3(1), 21–34, 2025.
Search in Google Scholar Back to article
Jahan M.I., Ullah M.S., Roshid H., Rahman Z., Akter R., Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying Different integration algorithms, International Journal of Mathematics and Computer in Engineering, 3(1), 1–12, 2025.
Search in Google Scholar Back to article
Omede B.I., Peter O.J., Atokolo W., Bolaji B., Ayoola T.A., A mathematical analysis of the two-strain tuberculosis model dynamics with exogenous re-infection, Healthcare Analytics, 4, 100266, 2023.
Search in Google Scholar Back to article
Chukwu C.W., Bonyah E., Juga M.L., Fatmawati, On mathematical modeling of fractional-order stochastic for tuberculosis transmission dynamics, Results in Control and Optimization, 11, 100238, 2023.
Search in Google Scholar Back to article
Lu J., Zhu L., Gao W., Remarks on bipolar cubic fuzzy graphs and its chemical applications, International Journal of Mathematics and Computer in Engineering, 1(1), 1–10, 2023.
Search in Google Scholar Back to article
Veeresha P., The efficient fractional order based approach to analyze chemical reaction associated with pattern formation, Chaos Solitons and Fractals, 165(2), 112862, 2022.
Search in Google Scholar Back to article
Altman B.J., Cancer clocks out for lunch: disruption of circadian rhythm and metabolic oscillation in cancer, Frontiers in Cell and Developmental Biology, 4(62), 1–9, 2016.
Search in Google Scholar Back to article
Tao G., Sirendaoerji, The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term, Chinese Physics, 15(12), 2809–2818, 2006.
Search in Google Scholar Back to article
Shen S.S., A Course on Nonlinear Waves, Springer, USA, 2012.
Search in Google Scholar Back to article
Zhang S., Exp-function method exactly solving a KdV equation with forcing term, Applied Mathematics and Computation, 197(1), 128–134, 2008.
Search in Google Scholar Back to article
Gao W., Ismael H.F., Husien A.M., Bulut H., Baskonus H.M., Optical soliton solutions of the nonlinear Schrödinger and resonant nonlinear Schrödinger equation with parabolic law, Applied Science, 10(1), 219, 2020.
Search in Google Scholar Back to article
Guirao J.L.G., Baskonus H.M., Kumar A., Rawat M.S., Yel G., Complex soliton solutions to the (3+1)-dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation, Symmetry, 12(1), 17, 2020.
Search in Google Scholar Back to article

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

Abstract

Paradigm

My account