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Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations
Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term
1. | Dpto. de Matemáticas, Universidad de Cádiz, Polígono del Río San Pedro s/n 11510 Puerto Real, Cádiz, Spain, Spain |
References:
[1] |
S. A. Anco and G. Bluman, Direct construction of conservation laws from field equations, Physical Review letters, 78 (1997), 2869-2873.
doi: 10.1103/PhysRevLett.78.2869. |
[2] |
S. C. Anco and G. Bluman, Direct constrution method for conservation laws for partial differential equations Part II: General treatment, Euro. J. of Applied Mathematics, 13 (2002), 567-585.
doi: 10.1017/S0956792501004661. |
[3] |
M. S. Bruzón, M. L. Gandarias and N. H. Ibragimov, Self-adjoint sub-classes of generalized thin film equations, J. Math. Anal. Appl., 357 (2009), 307-313.
doi: 10.1016/j.jmaa.2009.04.028. |
[4] |
J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., 1 (1948), 171-199. |
[5] |
C. R. Cattaneo, On a form of heat equation which eliminates the paradox of instantaneous propagation, Acad. Sci. Paris, (1895), 431-433. |
[6] |
N. Euler and M. Euler, On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations: two linearisable hierachies, Journal of Nonlinear Mathematical Physics, 16 (2009), 489-504.
doi: 10.1142/S1402925109000509. |
[7] |
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 355-369.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[8] |
M. L. Gandarias, Weak self-adjoint differential equations, J. Phys. A: Math. Theor., 44 (2011), 262001. |
[9] |
M. L. Gandarias, Weak self-adjointness and conservation laws for a porous medium equation, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 2342-2349.
doi: 10.1016/j.cnsns.2011.10.020. |
[10] |
M. L. Gandarias, Nonlinear self-adjointness through differential substitutions, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 3523-3528.
doi: 10.1016/j.cnsns.2014.02.013. |
[11] |
M. L. Gandarias, M. S. Bruzón and M. Rosa, Nonlinear self-adjointness and conservation laws for a generalized Fisher equation, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 1600-1606.
doi: 10.1016/j.cnsns.2012.11.023. |
[12] |
N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., 333 (2007), 311-328.
doi: 10.1016/j.jmaa.2006.10.078. |
[13] |
N. H. Ibragimov, Quasi-self-adjoint differential equations, Arch. ALGA, 4 (2007), 55-60. |
[14] |
N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math.Theor., 44 (2011), 432002.
doi: 10.1088/1751-8113/44/43/432002. |
[15] |
N. H. Ibragimov, M. Torrisi and R. Tracina, Self-adjointness and conservation laws of a generalized Burgers equation, J. Phys. A: Math. Theor., 44 (2011), 145201, 5pp.
doi: 10.1088/1751-8113/44/14/145201. |
[16] |
S. Kar, S. K. BaniK and D. S. Ray, Exact solutions of Fisher and Burgers equations with finite transport memory, J. Phys. A: Math. Gen., 36 (2003), 2771-2780.
doi: 10.1088/0305-4470/36/11/308. |
[17] |
A. Mishra and R. Kumar, Memory effects in Fisher equation with nonlinear convection term, Physics Letters A, 376 (2012), 1833-1835.
doi: 10.1016/j.physleta.2012.04.037. |
[18] |
M. Torrisi and R. Tracina, Quasi self-adjointness of a class of third order nonlinear dispersive equations, Nonlinear Analysis: Real World Applications, 14 (2013), 1496-1502.
doi: 10.1016/j.nonrwa.2012.10.013. |
[19] |
M. Wang, X. Li and J. Zhang, The $\frac{G'}G$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417-423.
doi: 10.1016/j.physleta.2007.07.051. |
show all references
References:
[1] |
S. A. Anco and G. Bluman, Direct construction of conservation laws from field equations, Physical Review letters, 78 (1997), 2869-2873.
doi: 10.1103/PhysRevLett.78.2869. |
[2] |
S. C. Anco and G. Bluman, Direct constrution method for conservation laws for partial differential equations Part II: General treatment, Euro. J. of Applied Mathematics, 13 (2002), 567-585.
doi: 10.1017/S0956792501004661. |
[3] |
M. S. Bruzón, M. L. Gandarias and N. H. Ibragimov, Self-adjoint sub-classes of generalized thin film equations, J. Math. Anal. Appl., 357 (2009), 307-313.
doi: 10.1016/j.jmaa.2009.04.028. |
[4] |
J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., 1 (1948), 171-199. |
[5] |
C. R. Cattaneo, On a form of heat equation which eliminates the paradox of instantaneous propagation, Acad. Sci. Paris, (1895), 431-433. |
[6] |
N. Euler and M. Euler, On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations: two linearisable hierachies, Journal of Nonlinear Mathematical Physics, 16 (2009), 489-504.
doi: 10.1142/S1402925109000509. |
[7] |
R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 355-369.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[8] |
M. L. Gandarias, Weak self-adjoint differential equations, J. Phys. A: Math. Theor., 44 (2011), 262001. |
[9] |
M. L. Gandarias, Weak self-adjointness and conservation laws for a porous medium equation, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 2342-2349.
doi: 10.1016/j.cnsns.2011.10.020. |
[10] |
M. L. Gandarias, Nonlinear self-adjointness through differential substitutions, Communications in Nonlinear Science and Numerical Simulation, 19 (2014), 3523-3528.
doi: 10.1016/j.cnsns.2014.02.013. |
[11] |
M. L. Gandarias, M. S. Bruzón and M. Rosa, Nonlinear self-adjointness and conservation laws for a generalized Fisher equation, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 1600-1606.
doi: 10.1016/j.cnsns.2012.11.023. |
[12] |
N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., 333 (2007), 311-328.
doi: 10.1016/j.jmaa.2006.10.078. |
[13] |
N. H. Ibragimov, Quasi-self-adjoint differential equations, Arch. ALGA, 4 (2007), 55-60. |
[14] |
N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math.Theor., 44 (2011), 432002.
doi: 10.1088/1751-8113/44/43/432002. |
[15] |
N. H. Ibragimov, M. Torrisi and R. Tracina, Self-adjointness and conservation laws of a generalized Burgers equation, J. Phys. A: Math. Theor., 44 (2011), 145201, 5pp.
doi: 10.1088/1751-8113/44/14/145201. |
[16] |
S. Kar, S. K. BaniK and D. S. Ray, Exact solutions of Fisher and Burgers equations with finite transport memory, J. Phys. A: Math. Gen., 36 (2003), 2771-2780.
doi: 10.1088/0305-4470/36/11/308. |
[17] |
A. Mishra and R. Kumar, Memory effects in Fisher equation with nonlinear convection term, Physics Letters A, 376 (2012), 1833-1835.
doi: 10.1016/j.physleta.2012.04.037. |
[18] |
M. Torrisi and R. Tracina, Quasi self-adjointness of a class of third order nonlinear dispersive equations, Nonlinear Analysis: Real World Applications, 14 (2013), 1496-1502.
doi: 10.1016/j.nonrwa.2012.10.013. |
[19] |
M. Wang, X. Li and J. Zhang, The $\frac{G'}G$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417-423.
doi: 10.1016/j.physleta.2007.07.051. |
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