Wazwaz, Abdul-Majid Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations. (English) Zbl 1187.35199 Phys. Lett., A 352, No. 6, 500-504 (2006). Summary: Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations are developed. Unlike the standard Degasperis-Procesi and Camassa-Holm equations, where multi-peakon solutions arise, the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons. The tanh method and the sine-cosine method are used to achieve this goal. Cited in 65 Documents MSC: 35Q51 Soliton equations 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:Degasperis-Procesi equation; Camassa-Holm equation; solitary wave solutions; sine-cosine method; tanh method PDFBibTeX XMLCite \textit{A.-M. Wazwaz}, Phys. Lett., A 352, No. 6, 500--504 (2006; Zbl 1187.35199) Full Text: DOI References: [1] Mustafa, O. G., J. Math. Phys., 12, 1, 10 (2005) [2] Lundmark, H.; Szmigielski, J., Inverse Problems, 19, 6, 1241 (2003) [3] Degasperis, A.; Procesi, M., (Asymptotic Integrability Symmetry and Perturbation Theory (2002), World Scientific), 23-27 · Zbl 0963.35167 [4] Shen, J.; Xu, W.; Li, W., Chaos Solitons Fractals, 27, 2, 413 (2006) [5] Chen, C.; Tang, M., Chaos Solitons Fractals, 27, 3, 698 (2006) [6] Camassa, R.; Holm, D., Phys. Rev. Lett., 71, 11, 1661 (1993) [7] Camassa, R., Discrete Continuous Dyn. System Ser. B, 3, 1, 115 (2003) [8] Liu, Z.; Wang, R.; Jing, Z., Chaos Solitons Fractals, 19, 1, 77 (2004) [9] Liu, Z.; Qian, T., Appl. Math. Model., 26, 473 (2002) [10] Qian, T.; Tang, M., Chaos Solitons Fractals, 12, 7, 1347 (2001) [11] Tian, L.; Song, X., Chaos Solitons Fractals, 19, 3, 621 (2004) [12] Malfliet, W.; Hereman, W., Phys. Scr., 54, 563 (1996) [13] Malfliet, W.; Hereman, W., Phys. Scr., 54, 569 (1996) [14] Wazwaz, A. M., Partial Differential Equations: Methods and Applications (2002), Balkema: Balkema The Netherlands · Zbl 0997.35083 [15] Wazwaz, A. M., Math. Comput. Simulation, 63, 1, 35 (2003) [16] Wazwaz, A. M., Appl. Math. Comput., 135, 2-3, 399 (2003) [17] Wazwaz, A. M., Appl. Math. Comput., 135, 2-3, 411 (2003) [18] Wazwaz, A. M., Math. Comput. Model., 37, 3-4, 333 (2003) 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.