Feng, Dahe; Li, Jibin; Lü, Junliang; He, Tianlan New explicit and exact solutions for a system of variant RLW equations. (English) Zbl 1139.35323 Appl. Math. Comput. 198, No. 2, 715-720 (2008). Summary: A system of regularized long wave equations are studied. With the aid of the mathematic software Maple and using the direct method, some new exact solutions: compactons, solitons, solitary patterns and periodic solutions are obtained. Cited in 6 Documents MSC: 35C05 Solutions to PDEs in closed form 35Q51 Soliton equations Keywords:\(R(m, n)\) equations; compacton; solitary pattern solution; periodic solution; regularized long wave equations; Maple Software:Maple PDF BibTeX XML Cite \textit{D. Feng} et al., Appl. Math. Comput. 198, No. 2, 715--720 (2008; Zbl 1139.35323) Full Text: DOI References: [1] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press: Cambridge University Press London · Zbl 0762.35001 [2] Matveev, V. B.; Salle, M. A., Darboux Transformation and Solitons (1991), Springer-Verlag: Springer-Verlag Berlin · Zbl 0744.35045 [3] Gu, C. H.; Hu, H. S.; Zhou, Z. X., Darboux Transformations in Soliton Theory and its Geometric Applications (1999), Shanghai Sci. Tech. Publ.: Shanghai Sci. Tech. Publ. Shanghai [4] Hirota, R.; Satsuma, J., Soliton solutions of a coupled KdV equation, Phys. Lett. A, 85, 407-408 (1981) [5] Olver, P. J., Applications of Lie Groups to Differential Equations (1993), Springer-Verlag: Springer-Verlag New York · Zbl 0785.58003 [6] Bluman, G. W.; Kumei, S., Symmetries and Differential Equations (1989), Springer-Verlag: Springer-Verlag Berlin · Zbl 0718.35004 [7] Li, J. B.; Li, M., Bounded travelling wave solutions for the \((n+1)\)-dimensional sine- and sinh-Gordon equations, Chaos Soliton. Fract., 25, 1037-1047 (2005) · Zbl 1070.35068 [8] Tian, L.; Yin, J., New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations, Chaos Soliton. Fract., 20, 289-299 (2004) · Zbl 1046.35101 [9] Wazwaz, A. M., Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation, Appl. Math. Comput., 134, 487-500 (2003) · Zbl 1027.35119 [10] Wazwaz, A. M., A sine-cosine method for handling nonlinear wave equations, Math. Comput. Model., 40, 499-508 (2004) · Zbl 1112.35352 [11] Wazwaz, A. M., Solitons and periodic solutions for the fifth-order KdV equation, Appl. Math. Lett., 19, 1162-1167 (2006) · Zbl 1179.35296 [12] Wazwaz, A. M., Analytic study on nonlinear variant of the RLW and the PHI-four equations, Commun. Nonlinear Sci. Numer. Simul., 12, 314-327 (2007) · Zbl 1109.35099 [13] Yan, Z. Y.; Zhang, H. Q., New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics, Phys. Lett. A, 252, 291-296 (1999) · Zbl 0938.35130 [14] Yan, Z. Y., New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations, Phys. Lett. A, 292, 100-106 (2001) · Zbl 1092.35524 [15] Fan, E. G., Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics, Chaos Soliton. Fract., 16, 819-839 (2003) · Zbl 1030.35136 [16] Zhang, S., New exact solutions of the KdV-Burgers-Kuramoto equation, Phys. Lett. A, 358, 414-420 (2006) · Zbl 1142.35592 [17] Wang, M. L., Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A, 213, 279-287 (1996) · Zbl 0972.35526 [18] Dye, J. M.; Parker, A., An inverse scattering scheme for the regularized long-wave equation, J. Math. Phys., 41, 2889-2904 (2000) · Zbl 0973.35165 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.