Chen, Yong; Li, Biao Symbolic computation and construction of soliton-like solutions to the \((2 + 1)\)-dimensional dispersive long-wave equations. (English) Zbl 1211.35234 Int. J. Eng. Sci. 42, No. 7, 715-724 (2004). Summary: By means of a new Riccati equation expansion method, we consider the \((2 + 1)\)-dimensional dispersive long-wave equations \(\eta_{y,t}+\eta_{xx}+1/2u^2_{xy}=0\), \(\eta_t+(u_{\eta}+u+u_{xy})_x=0\). As a result, we not only can successfully recover the previously known formal solutions obtained by known tanh function methods but also construct new and more general formal solutions. The solutions obtained include the nontravelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, triangular functions solutions. Cited in 3 Documents MSC: 35Q51 Soliton equations 35-04 Software, source code, etc. for problems pertaining to partial differential equations Software:Mathematica; Maple; PDEtools PDFBibTeX XMLCite \textit{Y. Chen} and \textit{B. Li}, Int. J. Eng. Sci. 42, No. 7, 715--724 (2004; Zbl 1211.35234) Full Text: DOI References: [1] Ablowitz, M. J.; Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press: Cambridge University Press New York · Zbl 0762.35001 [2] Parkes, E. J.; Duffy, B. R., Comput. Phys. Commun., 98, 288 (1996) [3] Parkes, E. J.; Duffy, B. R., Phys. Lett. A, 229, 217 (1997) · Zbl 1043.35521 [4] Khater, A. H.; Malfiet, W.; Callebaut, D. K.; Kamel, E. S., Chaos, Solitons Fractals, 14, 513 (2002) [5] Fan, E., Phys. Lett. A, 277, 212 (2000) [6] Fan, E., Z. Naturforsch. A, 56, 312 (2001) [7] Fan, E.; Zhang, J.; Hon, B. Y.C., Phys. Lett. A, 291, 376 (2001) [8] Elwakil, S. A.; El-labany, S. K.; Zahran, M. A.; Sabry, R., Phys. Lett. A, 299, 179 (2002) [9] Gao, Y. T.; Tian, B., Comput. Phys. Commun., 133, 158 (2001) [10] Tian, B.; Gao, Y. T., Z. Naturforsch. A, 57, 39 (2002) [11] Tian, B.; Zhao, K. Y.; Gao, Y. T., Int. J. Eng. Sci., 35, 1081 (1997) [12] Lou, S. Y.; Ruan, H. Y., J. Phys. A: Math. Gen., 35, 305 (2001) [13] Yan, Z. Y., Phys. Lett. A, 292, 100 (2001) [14] Yan, Z. Y.; Zhang, H. Q., Phys. Lett. A, 285, 355 (2001) [15] Chen, Y.; Yan, Z. Y.; Li, B.; Zhang, H. Q., Commun. Theor. Phys. (Beijing, China), 38, 261 (2002) [16] Li, B.; Chen, Y.; Zhang, H. Q., J. Phys. A: Math. Gen., 35, 8253 (2002) [17] Li, B.; Chen, Y.; Zhang, H. Q., Chaos, Solitons Fractals, 15, 647 (2003) [18] Inverse Probl., 3, 371 (1987) [19] Paquin, G.; Winternitz, P., Physica D, 46, 122 (1990) [20] Lou, S. Y., J. Phys. A: Math. Gen., 27, 3235 (1994) [21] Lou, S. Y., Math. Meth. Appl. Sci., 18, 789 (1995) [22] Lou, S. Y., Phys. Lett. A, 176, 96 (1993) [23] Tang, X. Y.; Chen, C. L.; Lou, S. Y., J. Phys. A: Math. Gen., 35, L293 (2002) [24] Tang, X. Y.; Lou, S. Y., Chaos, Solitons Fractals, 14, 1451 (2002) [25] Zhang, J. F., Commun. Theor. Phys. (Beijing, China), 37, 277 (2002) 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.