Artículos de revistas
Nonlinear Self-adjoint Classification Of A Burgers-kdv Family Of Equations
Registro en:
Abstract And Applied Analysis. Hindawi Publishing Corporation, v. 2014, n. , p. - , 2014.
10853375
10.1155/2014/804703
2-s2.0-84901001080
Autor
Sampaio J.C.S.
Freire I.L.
Institución
Resumen
The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out. © 2014 Júlio Cesar Santos Sampaio and Igor Leite Freire. 2014
Ibragimov, N.H., A new conservation theorem (2007) Journal of Mathematical Analysis and Applications, 333 (1), pp. 311-328. , 10.1016/j.jmaa.2006.10.078 MR2323493 ZBL1160.35008 Ibragimov, N.H., Integrating factors, adjoint equations and Lagrangians (2006) Journal of Mathematical Analysis and Applications, 318 (2), pp. 742-757. , 10.1016/j.jmaa.2005.11.012 MR2215182 ZBL1102.34002 Ibragimov, N.H., Nonlinear self-adjointness and conservation laws (2011) Journal of Physics A: Mathematical and Theoretical, 44. , 432002 10.1088/1751-8113/44/43/432002 Ibragimov, N.H., Nonlinear self-adjointness in constructing conservation laws (2011) Archives of ALGA, 7-8, pp. 1-90 Atherton, R.W., Homsy, G.M., On the existence and formulation of variational principles for nonlinear differential equations (1975) Stuides in Applied Mathematics, 54 (1), pp. 31-60. , MR0458271 ZBL0322.49019 Gandarias, M.L., Weak self-adjoint differential equations (2011) Journal of Physics A: Mathematical and Theoretical, 44 (26). , 262001 10.1088/1751-8113/44/26/262001 Bruzón, M.S., Gandarias, M.L., Ibragimov, N.H., Self-adjoint sub-classes of generalized thin film equations (2009) Journal of Mathematical Analysis and Applications, 357 (1), pp. 307-313. , 10.1016/j.jmaa.2009.04.028 MR2526830 ZBL1170.35439 Freire, I.L., Self-adjoint sub-classes of third and fourth-order evolution equations (2011) Applied Mathematics and Computation, 217 (22), pp. 9467-9473. , 10.1016/j.amc.2011.04.041 MR2804024 ZBL1219.35048 Gandarias, M.L., Redondo, M., Bruzón, M.S., Some weak self-adjoint Hamilton-Jacobi-Bellman equations arising in financial mathematics (2012) Nonlinear Analysis. Real World Applications, 13 (1), pp. 340-347. , 10.1016/j.nonrwa.2011.07.041 MR2846844 ZBL1238.35048 Gandarias, M.L., Bruzón, M.S., Some conservation laws for a forced KdV equation (2012) Nonlinear Analysis. Real World Applications, 13 (6), pp. 2692-2700. , 10.1016/j.nonrwa.2012.03.013 MR2927217 ZBL1268.35106 Gandarias, M.L., Weak self-adjointness and conservation laws for a porous medium equation (2012) Communications in Nonlinear Science and Numerical Simulation, 17 (6), pp. 2342-2349. , 10.1016/j.cnsns.2011.10.020 MR2877680 ZBL06056884 Johnpillai, A.G., Khalique, C.M., Conservation laws of KdV equation with time dependent coefficients (2011) Communications in Nonlinear Science and Numerical Simulation, 16 (8), pp. 3081-3089. , 10.1016/j.cnsns.2010.10.031 MR2782999 ZBL1219.35236 Gandarias, M.L., Bruzón, M.S., Conservation laws for a class of quasi self-adjoint third order equations (2012) Applied Mathematics and Computation, 219 (2), pp. 668-678. , 10.1016/j.amc.2012.06.059 MR2956996 Torrisi, M., Tracinà, R., Quasi self-adjointness of a class of third order nonlinear dispersive equations (2013) Nonlinear Analysis. Real World Applications, 14 (3), pp. 1496-1502. , 10.1016/j.nonrwa.2012.10.013 MR3004516 ZBL1261.35131 Freire, I.L., Santos Sampaio, J.C., On the nonlinear self-adjointness and local conservation laws for a class of evolution equations unifying many models (2014) Communications in Nonlinear Science and Numerical Simulation, 19 (2), pp. 350-360. , 10.1016/j.cnsns.2013.06.010 MR3142476 Freire, I.L., Sampaio, J.C.S., Nonlinear self-adjointness of a generalized fifth-order KdV equation (2012) Journal of Physics A: Mathematical and Theoretical, 45 (3). , 032001 10.1088/1751-8113/45/3/032001 MR2871416 ZBL1234.35221 Freire, I.L., New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order (2013) Communications in Nonlinear Science and Numerical Simulation, 18 (3), pp. 493-499. , 10.1016/j.cnsns.2012.08.022 MR2990691 ZBL06244246 Freire, I.L., Sampaio, J.C.S., A review on some results on local conservation laws for certain evolution equations (2013) TEMA. Tendências em Matemática Aplicada e Computacional, 14 (1), pp. 109-118. , 10.5540/tema.2013.014.01.0109 MR3064682 Freire, I.L., Conservation laws for self-adjoint first-order evolution equation (2011) Journal of Nonlinear Mathematical Physics, 18 (2), pp. 279-290. , 10.1142/S1402925111001453 MR2812420 ZBL1219.35228 Freire, I.L., New conservation laws for inviscid Burgers equation (2012) Computational & Applied Mathematics, 31 (3), pp. 559-567. , 10.1590/S1807-03022012000300007 MR3009189 ZBL1263.76057 Abdulwahhab, M.A., Conservation laws of inviscid Burgers equation with nonlinear damping (2014) Communications in Nonlinear Science and Numerical Simulation, 19 (6), pp. 1729-1741. , 10.1016/j.cnsns.2013.10.011 MR3144755 Ibragimov, N.H., Torrisi, M., Tracinà, R., Self-adjointness and conservation laws of a generalized Burgers equation (2011) Journal of Physics A: Mathematical and Theoretical, 44 (14). , 145201 10.1088/1751-8113/44/14/145201 MR2780416 ZBL1216.35115 Bozhkov, Y., Dimas, S., Ibragimov, N.H., Conservation laws for a coupled variable-coefficient modified Korteweg-de Vries system in a two-layer fluid model (2013) Communications in Nonlinear Science and Numerical Simulation, 18 (5), pp. 1127-1135. , 10.1016/j.cnsns.2012.09.015 MR2998573 ZBL1261.35127 Ibragimov, N.H., Torrisi, M., Tracinà, R., Quasi self-adjoint nonlinear wave equations (2010) Journal of Physics A: Mathematical and Theoretical, 43 (44). , 442001 10.1088/1751-8113/43/44/442001 MR2733811 ZBL1206.35174 Wang, Y., Wei, L., Self-adjointness, symmetries, and conservation laws for a class of wave equations incorporating dissipation (2013) Abstract and Applied Analysis, 2013, p. 6. , 407908 MR3064344 ZBL1275.35016 10.1155/2013/407908 Avdonina, E.D., Ibragimov, N.H., Conservation laws of anisotropic heat equations (2012) Archives of ALGA, 9, pp. 13-22 Avdonina, E.D., Ibragimov, N.H., Conservation laws and exact solutions for nonlinear diffusion in anisotropic media (2013) Communications in Nonlinear Science and Numerical Simulation, 18 (10), pp. 2595-2603. , 10.1016/j.cnsns.2013.02.009 MR3055035 Bozhkov, Y., Silva, K.A.A., Nonlinear self-adjointness of a 2D generalized second order evolution equation (2012) Nonlinear Analysis. Theory, Methods & Applications A, 75 (13), pp. 5069-5078. , 10.1016/j.na.2012.04.023 MR2927570 ZBL1246.35084 Bozhkov, Y., Dimas, S., Group classification and conservation laws for a two-dimensional generalized Kuramoto-Sivashinsky equation (2013) Nonlinear Analysis. Theory, Methods & Applications A, 84, pp. 117-135. , 10.1016/j.na.2013.02.010 MR3034576 ZBL1278.76097 Tracinà, R., On the nonlinear self-adjointness of the Zakharov-Kuznetsov equation (2014) Communications in Nonlinear Science and Numerical Simulation, 19 (2), pp. 377-382. , 10.1016/j.cnsns.2013.06.014 MR3142480 Gazeau, J.-P., Winternitz, P., Symmetries of variable coefficient Korteweg-de Vries equations (1992) Journal of Mathematical Physics, 33 (12), pp. 4087-4102. , 10.1063/1.529807 MR1191768 ZBL0767.35077 Güngör, F., Lahno, V.I., Zhdanov, R.Z., Symmetry classification of KdV-type nonlinear evolution equations (2004) Journal of Mathematical Physics, 45 (6), pp. 2280-2313. , 10.1063/1.1737811 MR2059693 ZBL1094.35007 Freire, I.L., Sampaio, J.C.S., Conservation Laws for A Burgers-KdV Family of Equations, , in preparation, 2014 Bluman, G.W., Anco, S.C., (2002) Symmetry and Integration Methods for Differential Equations, pp. x+419. , New York, NY, USA Springer MR1914342 Bluman, G.W., Kumei, S., (1989) Symmetries and Differential Equations, 81, pp. xiv+412. , New York, NY, USA Springer Applied Mathematical Sciences MR1006433 Ibragimov, N.H., (1985) Transformation Groups Applied to Mathematical Physics, pp. xv+394. , Dordrecht, The Netherlands D. Reidel Publishing Mathematics and its Applications (Soviet Series) Translated from the Russian MR785566 Olver, P.J., (1986) Applications of Lie Groups to Differential Equations, pp. xxvi+497. , New York, NY, USA Springer 10.1007/978-1-4684-0274-2 MR836734 Olver, P.J., Conservation laws and null divergences (1983) Mathematical Proceedings of the Cambridge Philosophical Society, 94 (3), pp. 529-540. , 10.1017/S030500410000092X MR720804 ZBL0556.35021 Olver, P.J., Conservation laws of free boundary problems and the classification of conservation laws for water waves (1983) Transactions of the American Mathematical Society, 277 (1), pp. 353-380. , 10.2307/1999361 MR690057 ZBL0519.76015 Popovych, R.O., Samoilenko, A.M., Local conservation laws of second-order evolution equations (2008) Journal of Physics A: Mathematical and Theoretical, 41 (36). , 362002 10.1088/1751-8113/41/36/362002 MR2447855 ZBL1146.37039 Popovych, R.O., Sergyeyev, A., Conservation laws and normal forms of evolution equations (2010) Physics Letters A, 374 (22), pp. 2210-2217. , 10.1016/j.physleta.2010.03.033 MR2629731 ZBL1237.35142 Vinogradov, A.M., Local symmetries and conservation laws (1984) Acta Applicandae Mathematicae, 2 (1), pp. 21-78. , 10.1007/BF01405491 MR736872 ZBL0547.58043 Ibragimov, N.H., Quasi-self-adjoint differential equations (2007) Archives of ALGA, 4, pp. 55-60 Zhang, Z.-Y., Approximate nonlinear self-adjointness and approximate conservation laws (2013) Journal of Physics A: Mathematical and Theoretical, 46 (15). , 155203 10.1088/1751-8113/46/15/155203 MR3043882 ZBL1267.81155 Alexandrova, A.A., Ibragimov, N.H., Lukashchuk, V.O., Group classification and conservation laws of nonlinear filtration equation with a small parameter (2014) Communications in Nonlinear Science and Numerical Simulation, 19 (2), pp. 364-370. , 10.1016/j.cnsns.2013.06.012 MR3142478 Lukashchulk, S.Yu., Constructing of Conservation Laws for Fractional Differential Equations, , 16a Mogran Conference, UFA, Russia, 2013 Da Silva, P.L., Freire, I.L., Strict Self-adjointness and Shallow Water Models, , http://arxiv.org/abs/1312.3992