Li, Yishen; Ma, Wen-Xiu; Zhang, Jin E. Darboux transformations of classical Boussinesq system and its new solutions. (English) Zbl 1115.35329 Phys. Lett., A 275, No. 1-2, 60-66 (2000). Summary: Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq system are considered in this letter. They are used to generate new solutions of the classical Boussinesq system. An interesting solution of double-peak soliton has been found. Cited in 1 ReviewCited in 54 Documents MSC: 35K15 Initial value problems for second-order parabolic equations 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35Q35 PDEs in connection with fluid mechanics 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems Keywords:Darboux transformation; soliton equation; exact solution PDFBibTeX XMLCite \textit{Y. Li} et al., Phys. Lett., A 275, No. 1--2, 60--66 (2000; Zbl 1115.35329) Full Text: DOI References: [1] T.Y. Wu, J.E. Zhang, On modelling a nonlinear long wave, in: Math is for Solving Problems, L.P. Cook, V. Roythurd, M. Tulin (Eds.), SIAM, 1996, p. 233-241.; T.Y. Wu, J.E. Zhang, On modelling a nonlinear long wave, in: Math is for Solving Problems, L.P. Cook, V. Roythurd, M. Tulin (Eds.), SIAM, 1996, p. 233-241. [2] Kaup, D. J., Prog. Theor. Phys., 54, 396 (1975) [3] Kupershmidt, B. A., Commun. Math. Phys., 99, 51 (1985) [4] Satsuma, J.; Kajiwara, K.; Matsukidaira, J.; Hietarinta, J., J. Phys. Soc. Jpn., 61, 3096 (1992) [5] Boiti, M.; Leon, J. J.P.; Pempinelli, F., Inv. Probl., 3, 37 (1987) [6] Konopelchenko, B. G., Inv. Probl., 4, 151 (1988) 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.