Journal of Vibration Testing and System Dynamics
Symmetry Analysis and Reductions Through Conservation Laws of a Generalized Bogoyavlensky-Konopelchenko Equation in $(2+1)$-Dimensions
Journal of Vibration Testing and System Dynamics 5(3) (2021) 249--257 | DOI:10.5890/JVTSD.2021.09.005
M.S. Bruz 'on, M.L. Gandarias
Department of Mathematics, Faculty of Science, C'adiz University, Puerto Real, 11510, Spain
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Abstract
In this paper we obtain Lie symmetries and travelling wave solutions for a generalized Bogoyavlensky-Konopelchenko equation in $(2+1)$-dimensions.
Moreover, we determine some low-order conservation laws which are invariant under the translation symmetry;
consequently they are inherited by the reduced differential equations.
References
-
[1]  | Ray, S.S. (2017), On conservation laws by Lie symmetry analysis for (2+1)-dimensional Bogoyavlensky-Konopelchenko equation in wave propagation, Computers and Mathematics with Applications,
74(6), 1158-1165.
|
-
[2]  | Li, Q., Chaolu, T., and Wanga, Y.H. (2019), Lump-type solutions and lump solutions for the (2+1)-dimensional generalized
Bogoyavlensky-Konopelchenko equation., Computers and Mathematics with Applications, 77, 2077-2085
|
-
[3]  | Bruz\on, M.S. and Gandarias, M.L. (2003), Symmetry Reductions for a
Dissipation-Modified KdV Equation,
Applied Mathematics Letters, 16, 55-159.
|
-
[4]  | Bruz\on, M.S., de la Rosa, R., and Tracin\`a, R. (2018), Exact solutions via equivalence transformations of variable-coefficient fifth-order KdV equations, Applied Mathematics and Computation, 325, 239-245.
|
-
[5]  | Bruz\on, M.S., M\arquez, A.P., Garrido, T.M., Recio, E., and de la Rosa, R. (2019), Conservation laws for a generalized seventh order {KdV} equation, Journal of Computational and Applied Mathematicsn, 354, 682-788.
|
-
[6]  | de la Rosa, R., Recio, E., Garrido, T.M., and Bruz\on,
M.S. (2019), Lie symmetry analysis of (2+1)-dimensional {KdV} equations with variable coefficients, International Journal of Computer Mathematics, 97(1-2), 330-340.
|
-
[7]  | Anco, S. and Bluman, G. (1997), Direct constrution of conservation laws from field equations, Phys. Rev. Lett., 78, 2869-2873.
|
-
[8]  | Anco, S.C. and Bluman, G. (2002), Direct constrution method for conservation laws of partial differential equations Part I: Examples of conservation law
classifications, Eur. J. Appl. Math., 13, 545-566.
|
-
[9]  | Anco, S.C. and Bluman, G. (2002), Direct constrution method for conservation laws for partial differential equations Part II: General treatment, Eur. J. Appl. Math.,
41, 567-585.
|
-
[10]  |
Anco, S.C. (2016),
Symmetry properties of conservation laws,
Internat, J. Modern Phys. B, 30, 1640003.
|
-
[11]  |
Anco, S.C. (2017),
Generalization of Noethers theorem in modern form to non-variational partial differential equations,
In: Recent progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, 119-182,
Fields Institute Communications, Volume 79.
|
-
[12]  | Ibragimov, N.H. (2007), Quasi self-adjoint differential equations, Arch. ALGA, 4, 55-60.
|
-
[13]  | Ibragimov, N.H. (2007), A new conservation theorem, Journal of Mathematical Analysis and Applications,
333, 311-328.
|
-
[14]  | Bruz\on, M.S., Gandarias, M.L., and Ibragimov, N.H. (2009), Self-adjoint sub-classes of generalized thin film equations,
J. Math. Anal. Appl., 357, 307-313.
|
-
[15]  | Anco, S.C., Gandarias, M.L., and Recio, E. (2018), Conservation laws, symmetries, and line soliton solutions of
generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions, { Theor. Math.
Phys.}, 197(1), 1393-1411.
|
-
[16]  |
Anco, S.C. and Gandarias, M.L.
Multi-reduction theory for PDEs with conservation laws.
Comunications in Nonlinear Science and Numerical Simulations (Accepted).
|
-
[17]  |
Anco, S.C. and Kara, A. (2018),
Symmetry invariance of conservation laws,
Euro. J. Appl. Math., 29(1), 78-117.
|
-
[18]  |
Bluman, G. and Anco, S.C. (2006),
New conservation laws obtained directly from symmetry action on known conservation laws,
{ J. Math. Anal. Appl.}, 322, 233-250.
|
-
[19]  |
Bokhari, A.H., Dweik, A.Y., Zaman, F.D., Kara, A.H., and Mahomed, F.M. (2010),
Generalization of the double reduction theory,
Nonlinear Analysis: Real World Applications, 11(5), 3763-3769.
|
-
[20]  |
Gandarias, M.L. and Rosa, M. (2016),
On double reductions from symmetries and conservation laws for a damped Boussinesq equation,
Chaos, Solitons, Fractals, 89, 560-565.
|
-
[21]  |
Gandarias, M.L. and Bruz\on, M.S. (2017),
Conservation laws for a Boussinesq equation,
Appl. Math. and Nonlin. Sci., 2(2), 465-472.
|
-
[22]  | Halder, A.K., Paliathanasis, A., and Leach, P.G.L. (2020), Similarity solutions and Conservation laws for the
Bogoyavlensky-Konopelchenko Equation by Lie point symmetries arXiv:2003.10131v1.
|
-
[23]  | Ibragimov, N.H., Torrisi, M., and Tracina, R. (2010), Quasi self-adjoint nonlinear wave equations, J. Phys. A: Math.
Theor., 43, 442001.
|
-
[24]  | Ibragimov, N.H. (2006), Integrating factors, adjoint equations and Lagrangians, J. Math. Anal. Appl., 318, 742-757.
|
-
[25]  | Ibragimov, N.H. (2006), The answer to the question put to me by LV Ovsiannikov 33 years ago, Arch.
ALGA, 3, 53-80.
|
-
[26]  | Ibragimov, N.H. (2011), Nonlinear self-adjointness in constructing conservation laws, Arch. ALGA, 8, 59-63.
|
-
[27]  | Ray, S.S. (2018), Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach, Modern Physics Letters B, 32(11), 1850127.
|
-
[28]  |
San, S., Akbulut, A., \"Unsal, \"O., and Ta, F. (2017),
Conservation laws and double reduction of(2+1) dimensional Calogero-Bogoyavlenskii-Schiff equation,
Math. Meth. Appl. Sci., 40, 1703-1710.
|
-
[29]  |
Sj\"oberg, A. (2007),
Double reduction of PDEs from the association of symmetries with conservation laws with applications,
Appl. Math. Comput., 184, 608-616.
|
-
[30]  |
Sj\"oberg, A. (2009),
On double reduction from symmetries and conservation laws,
Nonlinear Analysis: Real World Applications, 10, 3472-3477.
|