Wazwaz, Abdul-Majid New solitons and kinks solutions to the Sharma-Tasso-Olver equation. (English) Zbl 1118.65113 Appl. Math. Comput. 188, No. 2, 1205-1213 (2007). Summary: The Sharma-Tasso-Olver equation is investigated. The tanh method, the extended tanh method, and other ansatze involving hyperbolic and exponential functions are efficiently used for analytic study of this equation. New solitons and kinks solutions are formally derived. The proposed schemes are reliable and manageable. Cited in 1 ReviewCited in 33 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35Q51 Soliton equations Keywords:tanh method; hyperbolic functions ansatz; solitons; kinks PDFBibTeX XMLCite \textit{A.-M. Wazwaz}, Appl. Math. Comput. 188, No. 2, 1205--1213 (2007; Zbl 1118.65113) Full Text: DOI References: [1] Yan, Z., Integrability for two types of the (2+1)-dimensional generalized Sharma-Tasso-Olver integro-differential equations, MM Res., 22, 302-324 (2003) [2] Lian, Z.; Lou, S. Y., Symmetries and exact solutions of the Sharma-Tasso-Olver equation, Nonlinear Anal., 63, 1167-1177 (2005) [3] Wang, S.; Tang, X.; Lou, S. Y., Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation, Chaos, Solitons & Fractals, 21, 231-239 (2004) · Zbl 1046.35093 [4] Klaus, M.; Pelinovsky, D.; Rothos, V., Evans function for Lax operators with algebraically decaying potentials, J. Nonlinear Sci., 7, 1-44 (2005) · Zbl 1117.35070 [5] Whitham, G. B., Linear and Nonlinear Waves (1999), Wiley: Wiley New York · Zbl 0373.76001 [6] Kichenassamy, S.; Olver, P., Existence and nonexistence of solitary wave solutions to higher-order model evolution equations, SIAM J. Math. Anal., 23, 5, 1141-1166 (1992) · Zbl 0755.76023 [7] Rosenau, P.; Hyman, J. M., Compactons: solitons with finite wavelengths, Phys. Rev. Lett., 70, 5, 564-567 (1993) · Zbl 0952.35502 [8] Rosenau, P.; Pikovsky, A., Phase compactons in chains of dispersively coupled oscillations, Phys. Rev. Lett., 94, 174102, 1-4 (2005) [9] Baldwin, D.; Goktas, U.; Hereman, W.; Hong, L.; Martino, R. S.; Miller, J. C., Symbolic computation of exact solutions in hyperbolic and elliptic functions for nonlinear PDEs, J. Symbol. Comput., 37, 669-705 (2004) · Zbl 1137.35324 [10] Goktas, U.; Hereman, W., Symbolic computation of conserved densities for systems of nonlinear evolution equations, J. Symbol. Comput., 24, 591-621 (1997) · Zbl 0891.65129 [11] Malfliet, W., Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, 7, 650-654 (1992) · Zbl 1219.35246 [12] Malfliet, W., The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations, J. Comput. Appl. Math., 164-165, 529-541 (2004) · Zbl 1038.65102 [13] Wazwaz, A. M., The tanh method for travelling wave solutions of nonlinear equations, Appl. Math. Comput., 154, 3, 713-723 (2004) · Zbl 1054.65106 [14] Wazwaz, A. M., Partial Differential Equations: Methods and Applications (2002), Balkema Publishers: Balkema Publishers The Netherlands · Zbl 0997.35083 [15] Wazwaz, A. M., Compactons in a class of nonlinear dispersive equations, Math. Comput. Model., 37, 3/4, 333-341 (2003) · Zbl 1044.35078 [16] Wazwaz, A. M., Distinct variants of the KdV equation with compact and noncompact structures, Appl. Math. Comput., 150, 365-377 (2004) · Zbl 1039.35110 [17] Wazwaz, A. M., Variants of the generalized KdV equation with compact and noncompact structures, Comput. Math. Appl., 47, 583-591 (2004) · Zbl 1062.35120 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.