Zayed, E. M. E.; Abourabia, A. M.; Gepreel, Khaled A.; Horbaty, M. M. El On the rational solitary wave solutions for the nonlinear Hirota-Satsuma coupled KdV system. (English) Zbl 1106.35088 Appl. Anal. 85, No. 6-7, 751-768 (2006). Summary: The objective is to investigate an algebraic method for constructing new rational exact wave soliton solutions in terms of hyperbolic and triangular functions for the generalized nonlinear Hirota-Satsuma coupled KdV systems of partial differential equations using symbolic software like Mathematica or Maple. These studies reveal that the generalized nonlinear Hirota-Satsuma coupled KdV system has a rich variety of solutions. Cited in 7 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 35C05 Solutions to PDEs in closed form Keywords:rational solitary wave solutions; symbolic computation Software:Maple; Mathematica PDF BibTeX XML Cite \textit{E. M. E. Zayed} et al., Appl. Anal. 85, No. 6--7, 751--768 (2006; Zbl 1106.35088) Full Text: DOI OpenURL References: [1] Chenglin Bai, PhysicsLetter A 288 pp 191– (2002) [2] DOI: 10.1016/S0375-9601(02)00151-2 · Zbl 0996.34001 [3] DOI: 10.1016/S0375-9601(01)00161-X · Zbl 0984.37092 [4] DOI: 10.1016/S0375-9601(01)00815-5 · Zbl 1098.35559 [5] DOI: 10.1016/S0375-9601(02)00737-5 · Zbl 0996.35044 [6] Hirota R, Journal of the Physical Society of Japan 51 pp 3390– (1983) [7] DOI: 10.1016/S0960-0779(03)00099-7 · Zbl 1068.35130 [8] DOI: 10.1016/j.chaos.2003.09.042 · Zbl 1049.35156 [9] DOI: 10.1088/0305-4470/35/39/309 · Zbl 1040.35100 [10] DOI: 10.1016/S0375-9601(02)00517-0 · Zbl 0995.35061 [11] DOI: 10.1016/S0375-9601(99)00163-2 · Zbl 0935.37029 [12] DOI: 10.1016/j.chaos.2003.09.004 · Zbl 1049.35164 [13] DOI: 10.1016/j.chaos.2003.12.045 · Zbl 1069.35080 [14] DOI: 10.1080/00036810410001689274 · Zbl 1061.35072 [15] Zayed EME, International Journal of Nonlinear Sciences and Numerical Simulation 5 pp 221– (2004) · Zbl 1401.35014 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.