Girgis, Laila; Biswas, Anjan Soliton perturbation theory for nonlinear wave equations. (English) Zbl 1192.35150 Appl. Math. Comput. 216, No. 7, 2226-2231 (2010). Summary: This paper studies the soliton perturbation that are described by three nonlinear wave equations. The adiabatic dynamics of the soliton parameters and the soliton velocity is obtained, in the presence of perturbation terms. The fixed point is also determined in a couple of cases. Cited in 10 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations 35B20 Perturbations in context of PDEs Keywords:solitons; perturbation; fixed point PDFBibTeX XMLCite \textit{L. Girgis} and \textit{A. Biswas}, Appl. Math. Comput. 216, No. 7, 2226--2231 (2010; Zbl 1192.35150) 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 [4] Krishnan, E. V.; Khan, Q. J.A., Higher-order KdV-type equations and their stability, International Journal of Mathematics and Mathematical Sciences, 27, 4, 215-220 (2001) · Zbl 0991.35078 [6] Triki, H.; Wazwaz, A. M., Bright and dark soliton solutions for a \(K(m,n)\) equation with \(t\)-dependent coefficients, Physics Letters A, 373, 25, 2162-2165 (2009) · Zbl 1229.35232 [7] Wazwaz, A. M., New solitons and kink solutions for the Gardner equation, Communications in Nonlinear Science and Numerical Simulation, 12, 8, 1395-1404 (2007) · Zbl 1118.35352 [8] Wazwaz, A. M., New sets of solitary wave solutions to the KdV, mKdV and the generalized KdV equations, Communications in Nonlinear Science and Numerical Simulation, 13, 2, 331-339 (2008) · Zbl 1131.35385 [9] Yang, X. L.; Tang, J. S.; Qiao, Z., Traveling wave solutions of the generalized BBM equation, Pacific Journal of Applied Mathematics, 1, 3, 221-234 (2009) · Zbl 1356.35083 [10] Zhao, X.; Xu, W., Travelling wave solutions for a class of the generalized Benjamin-Bona-Mahoney equation, Applied Mathematics and Computation, 192, 2, 507-519 (2007) · Zbl 1193.35175 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.