Adem, Khadijo Rashid; Khalique, Chaudry Masood Exact solutions and conservation laws of a \((2 + 1)\)-dimensional nonlinear KP-BBM equation. (English) Zbl 1291.35271 Abstr. Appl. Anal. 2013, Article ID 791863, 5 p. (2013). Summary: We study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method. Cited in 8 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35A30 Geometric theory, characteristics, transformations in context of PDEs 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Wang, M.; Li, X.; Zhang, J., The \(\left(G^\prime / G\right)\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, 372, 4, 417-423 (2008) · Zbl 1217.76023 · doi:10.1016/j.physleta.2007.07.051 [2] Wazwaz, A. M., Exact solutions of compact and noncompact structures for the KP-BBM equation, Applied Mathematics and Computation, 169, 1, 700-712 (2005) · Zbl 1330.35059 · doi:10.1016/j.amc.2004.09.061 [3] Wazwaz, A. M., The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations, Chaos, Solitons and Fractals, 38, 5, 1505-1516 (2008) · Zbl 1154.35443 · doi:10.1016/j.chaos.2007.01.135 [4] Abdou, M. A., Exact periodic wave solutions to some nonlinear evolution equations, International Journal of Nonlinear Science, 6, 2, 145-153 (2008) · Zbl 1285.35089 [5] Song, M.; Yang, C.; Zhang, B., Exact solitary wave solutions of the Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation, Applied Mathematics and Computation, 217, 4, 1334-1339 (2010) · Zbl 1203.35245 · doi:10.1016/j.amc.2009.05.007 [6] Bluman, G. W.; Kumei, S., Symmetries and Differential Equations. Symmetries and Differential Equations, Applied Mathematical Sciences, 81 (1989), New York, NY, USA: Springer, New York, NY, USA · Zbl 0698.35001 [7] Olver, P. J., Applications of Lie Groups to Differential Equations. Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 107 (1993), Berlin, Germany: Springer, Berlin, Germany · Zbl 0785.58003 · doi:10.1007/978-1-4612-4350-2 [8] Ovsiannikov, L. V., Group Analysis of Differential Equations (1982), New York, NY, USA: Academic Press, New York, NY, USA · Zbl 0485.58002 [9] Ibragimov, N. H., CRC Handbook of Lie Group Analysis of Differential Equations, 1-3 (1994-1996), Boca Raton, Fla, USA: CRC Press, Boca Raton, Fla, USA · Zbl 0864.35001 [10] Kudryashov, N. A., Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, 24, 5, 1217-1231 (2005) · Zbl 1069.35018 · doi:10.1016/j.chaos.2004.09.109 [11] Anco, S. C.; Bluman, G., Direct construction method for conservation laws of partial differential equations—I: examples of conservation law classifications, European Journal of Applied Mathematics, 13, 5, 545-566 (2002) · Zbl 1034.35071 · doi:10.1017/S0956792501004661 [12] Vitanov, N. K., Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity, Communications in Nonlinear Science and Numerical Simulation, 15, 8, 2050-2060 (2010) · Zbl 1222.35062 · doi:10.1016/j.cnsns.2009.08.011 [13] Adem, A. R.; Khalique, C. M., Symmetry reductions, exact solutions and conservation laws of a new coupled KdV system, Communications in Nonlinear Science and Numerical Simulation, 17, 9, 3465-3475 (2012) · Zbl 1248.35180 · doi:10.1016/j.cnsns.2012.01.010 [14] Anthonyrajah, M.; Mason, D. P., Conservation laws and invariant solutions in the Fanno model for turbulent compressible flow, Mathematical & Computational Applications, 15, 4, 529-542 (2010) · Zbl 1371.76107 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.