RT journal article
T1 Symmetry Analysis, Exact Solutions and Conservation Laws of a Benjamin-Bona-Mahony-Burgers Equation in 2+1-Dimensions
A1 Bruzón Gallego, María de los Santos
A1 Garrido Letrán, Tamara María
A1 Rosa Silva, Rafael de la
A2 Matemáticas
K1 conservation laws
K1 exact solutions
K1 Lie symmetries
K1 symmetry reductions
AB The Benjamin-Bona-Mahony equation describes the unidirectional propagation of small-amplitude long waves on the surface of water in a channel. In this paper, we consider a family of generalized Benjamin-Bona-Mahony-Burgers equations depending on three arbitrary constants and an arbitrary function G(u). We study this family from the standpoint of the theory of symmetry reductions of partial differential equations. Firstly, we obtain the Lie point symmetries admitted by the considered family. Moreover, taking into account the admitted point symmetries, we perform symmetry reductions. In particular, for G & PRIME;(u)& NOTEQUAL;0, we construct an optimal system of one-dimensional subalgebras for each maximal Lie algebra and deduce the corresponding (1+1)-dimensional nonlinear third-order partial differential equations. Then, we apply Kudryashov's method to look for exact solutions of the nonlinear differential equation. We also determine line soliton solutions of the family of equations in a particular case. Lastly, through the multipliers method, we have constructed low-order conservation laws admitted by the family of equations.
PB MDPI
SN 2073-8994
YR 2021
FD 2021-11
LK http://hdl.handle.net/10498/26172
UL http://hdl.handle.net/10498/26172
LA eng
NO The authors acknowledge the financial support from Junta de Andalucia group FQM-201. The authors warmly thank the referees for their valuable comments and recommending changes that significantly improved this paper. In memory of Maria de los Santos Bruzon Gallego: thank you for dedicating your time and effort to care us and help us. You will always be our role model. May Maruchi rest in peace.
DS Repositorio Institucional de la Universidad de Cádiz
RD 13-nov-2026