Alka, W.; Goyal, Amit; Kumar, C. Nagaraja Nonlinear dynamics of DNA – Riccati generalized solitary wave solutions. (English) Zbl 1241.35205 Phys. Lett., A 375, No. 3, 480-483 (2011). Summary: We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of M. Peyrard and A. R. Bishop [in: Nonlinear coherent structures, Proc. 6th Interdisciplinary Workshop, Montpellier/Fr, 1989. Lect. Notes Phys. 353, 29–41 (1990; Zbl 0732.92004)]. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method. Cited in 9 Documents MSC: 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35L75 Higher-order nonlinear hyperbolic equations 35C08 Soliton solutions 74B20 Nonlinear elasticity 92D20 Protein sequences, DNA sequences Keywords:nonlinear dynamics; solitary wave solution; factorization method; Riccati generalization Citations:Zbl 0732.92004 PDFBibTeX XMLCite \textit{W. Alka} et al., Phys. Lett., A 375, No. 3, 480--483 (2011; Zbl 1241.35205) Full Text: DOI References: [1] Peyrard, M.; López, S. C.; James, G., Nonlinearity, 21, T91 (2008) [2] Watson, J. D.; Crick, F. H.C., Nature, 171, 737 (1953) [3] Yakushevich, L. V., Nonlinear Physics of DNA (2004), Wiley-VCH, John Wiley and Sons Ltd.: Wiley-VCH, John Wiley and Sons Ltd. Berlin · Zbl 0913.92001 [4] Davydov, A. S., Phys. Scr., 20, 387 (1979) [5] Englander, S. W.; Kallenbanch, N. R.; Heeger, A. J.; Krumhansl, J. A.; Litwin, S., Proc. Natl. Acad. Sci. USA, 77, 7222 (1980) [6] Yomosa, S., Phys. Rev. A, 27, 2120 (1983) [7] Takeno, S.; Homma, S., Prog. Theor. Phys., 72, 679 (1984) [8] Dauxois, T.; Peyrard, M.; Bishop, A. R., Phys. Rev. E, 47, R44 (1993) [9] Muto, V.; Lomdahl, P. S.; Christiansen, P. L., Phys. Rev. A, 42, 7452 (1990) [10] Yakushevich, L. V.; Savin, A. V.; Manevitch, L. I., Phys. Rev. E, 66, 016614 (2002) [11] Hien, D. L.; Nhan, N. T.; Ngo, V. T.; Viet, N. A., Phys. Rev. E, 76, 021921 (2007) [12] Daniel, M.; Vasumathi, M., Physica D, 231, 10 (2007) [13] Tabi, C. B.; Mohamadou, A.; Kofané, T. C., Phys. Lett. A, 373, 2476 (2009) · Zbl 1231.92033 [14] Zdravković, S.; Satarić, M. V., Phys. Lett. A, 373, 2739 (2009) · Zbl 1231.92016 [15] Jensen, P.; Jaric, M. V.; Bennemann, K. H., Phys. Lett. A, 95, 204 (1983) [16] Khan, A.; Bhaumik, D.; Dutta-Roy, B., Bull. Math. Biol., 47, 783 (1985) [17] Polozov, R. V.; Yakushevich, L. V., J. Theoret. Biol., 130, 423 (1988) [18] Gonzalez, J. A.; Landrove, M. M., Phys. Lett. A, 292, 256 (2002) [19] Yakushevich, L. V., Nanobiology, 1, 343 (1992) [20] Kalosakas, G.; Rasmussen, K. Q.; Bishop, A. R., Synth. Met., 141, 93 (2004) [21] Qian, X. M.; Lou, S. Y., Commun. Theor. Phys., 39, 501 (2003) [22] Infeld, L.; Hull, T. E., Rev. Mod. Phys., 23, 21 (1951) [23] Mielnik, B., J. Math. Phys., 25, 3387 (1984) [24] Cornejo-Pérez, O.; Rosu, H. C., Prog. Theor. Phys., 114, 533 (2005) [25] Reyes, M. A.; Rosu, H. C., J. Phys. A, 41, 285206 (2008) [26] Kong, D. X.; Lou, S. Y.; Zeng, J., Commun. Theor. Phys., 36, 737 (2001) [27] Forinash, K.; Bishop, A. R.; Lomdahl, P. S., Phys. Rev. B, 43, 10743 (1991) 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.