Triki, Houria; Hayat, T.; Aldossary, Omar M.; Biswas, Anjan Solitary wave and shock wave solutions to a second order wave equation of Korteweg-de Vries type. (English) Zbl 1219.35260 Appl. Math. Comput. 217, No. 21, 8852-8855 (2011). Summary: This paper obtains the solitary wave as well as the shock wave solutions to the second order wave equation of Korteweg-de Vries type that was first proposed in 2002. The ansatz method is used to retrieve these solutions. The domain restrictions as well as the parameter regimes are all identified in the process of obtaining the solution. Cited in 3 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35C08 Soliton solutions 35A22 Transform methods (e.g., integral transforms) applied to PDEs Keywords:evolution equations; solitons; integrability PDFBibTeX XMLCite \textit{H. Triki} et al., Appl. Math. Comput. 217, No. 21, 8852--8855 (2011; Zbl 1219.35260) Full Text: DOI References: [1] Antonova, M.; Biswas, A., Adiabatic parameter dynamics of perturbed solitary waves, Communications in Nonlinear Science and Numerical Simulation, 14, 3, 734-748 (2009) · Zbl 1221.35321 [2] Biswas, A., 1-Soliton solution of the \(K(m,n)\) equation with generalized evolution, Physics Letters A, 372, 25, 4601-4602 (2008) · Zbl 1221.35099 [3] Ismail, M. S., Numerical solution of complex modified Korteweg-de Vries equation by collocation method, Communications in Nonlinear Science and Numerical Simulation, 14, 3, 749-759 (2009) · Zbl 1221.65262 [4] Jibin, L.; Zhenrong, L., Smooth and non-smooth travelling waves in a nonlinearly dispersive equation, Applied Mathematical Modelling, 25, 1, 41-56 (2000) · Zbl 0985.37072 [5] Tzirtzilakis, E.; Xenos, M.; Marinakis, V.; Bountis, T., Interactions and stability of solitary waves in shallow water, Chaos, Solitons & Fractals, 14, 1, 87-95 (2002) · Zbl 1068.76011 [6] Tzirtzilakis, E.; Marinakis, V.; Apokis, C.; Bountis, T., Soliton-like solutions of higher order wave equations of Korteweg-de Vries type, Journal of Mathematical Physics, 43, 12, 6151-6161 (2002) · Zbl 1060.35127 [7] Wazwaz, A. M., A study on KdV and Gardner equations with time-dependent coefficients and forcing terms, Applied Mathematics and Computation, 217, 5, 2277-2281 (2010) · Zbl 1202.35266 [8] Yao, L.; Weiguo, R.; Bin, H., Traveling wave solutions for higher order wave equations of KdV type, Chaos, Solitons & Fractals, 23, 2, 469-475 (2005) · Zbl 1069.35075 [9] Yao, L.; Ji-bin, L.; Wei-guo, R.; Bin, H., Travelling wave solutions for a second order wave equation of KdV type, Applied Mathematics and Mechanics, 28, 11, 1455-1465 (2007) · Zbl 1231.35035 [10] Zhang, J.; Wu, F., A simple method to construct soliton-like solution of the general KdV equation with external force, Communications in Nonlinear Science and Numerical Simulation, 5, 4, 170-173 (2000) · Zbl 0986.35102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.