Kaya, Doğan The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. (English) Zbl 1195.35264 Phys. Lett., A 348, No. 3-6, 244-250 (2006). Summary: A decomposition method for approximating the solution of the generalized modified Boussinesq equation is implemented. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the decomposition series. The obtained results are found to be in good agreement with the exact solution. Cited in 9 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35C10 Series solutions to PDEs 35Q51 Soliton equations 35B45 A priori estimates in context of PDEs Keywords:decomposition method; generalized modified Boussinesq equation; traveling wave solution; solitary wave solution PDFBibTeX XMLCite \textit{D. Kaya}, Phys. Lett., A 348, No. 3--6, 244--250 (2006; Zbl 1195.35264) Full Text: DOI References: [1] Clarkson, P. A.; Le Veque, R. J.; Saxton, R., Stud. Appl. Math., 75, 95 (1986) [2] Saxton, R., J. Math. Anal. Appl., 105, 59 (1985) [3] Bogolubsky, I. L., Comput. Phys. Commun., 13, 149 (1977) [4] Li, J.; Zhang, L., Chaos Solitons Fractal, 14, 581 (2002) [5] Zhang, W.; Ma, W., Appl. Math. Mech., 20, 666 (1999) [6] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · Zbl 0802.65122 [7] Adomian, G., J. Math. Anal. Appl., 135, 501 (1988) [8] Wazwaz, A. M., Appl. Math. Comput., 102, 77 (1999) [9] Zhang, W.; Chang, Q.; Fan, E., J. Math. Anal. Appl., 287, 118 (2003) [10] Seng, V.; Abbaoui, K.; Cherruault, Y., Math. Comput. Modelling, 24, 59 (1996) [11] Cherruault, Y., Kybernetes, 18, 31 (1989) [12] Rèpaci, A., Appl. Math. Lett., 3, 35 (1990) [13] Cherruault, Y.; Adomian, G., Math. Comput. Modelling, 18, 103 (1993) [14] Abbaoui, K.; Cherruault, Y., Comput. Math. Appl., 28, 103 (1994) [15] Abbaoui, K.; Cherruault, Y., Comput. Math. Appl., 29, 103 (1995) [16] Abbaoui, K.; Pujol, M. J.; Cherruault, Y.; Himoun, N.; Grimalt, P., Kybernetes, 30, 1183 (2001) [17] Shawagfeh, N., J. Math. Phys., 34, 4364 (1993) [18] Adomian, G.; Rach, R.; Shawagfeh, N., Found. Phys. Lett., 8, 161 (1995) [19] Kaya, D., Int. J. Comput. Math., 75, 235 (2000) [20] Kaya, D., J. Appl. Math., 1, 29 (2001) [21] Kaya, D., Int. J. Comput. Math., 72, 531 (1999) [22] Kaya, D.; Aassila, M., Phys. Lett. A, 299, 201 (2002) [23] Kaya, D., Bull. Malaysian Math. Soc., 21, 95 (1998) [24] Kaya, D., Int. J. Comput. Math., 75, 235 (2000) [25] Kaya, D., Bull. Inst. Math. Acad. Sinica, 28, 51 (2000) [26] Kaya, D., Balkan Phys. Lett., 8, 100 (2000) [27] Kaya, D.; El-Sayed, S. M., Chaos Solitons Fractals, 17, 869 (2003) [28] Kaya, D.; El-Sayed, S. M., Phys. Lett. A, 310, 44 (2003) [29] El-Sayed, S. M.; Kaya, D., Appl. Math. Comput., 150, 763 (2004) 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.