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Shaban, Somayeh, Nadjafikhah, Mehdi. (1401). Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations. نشریه مهندسی عمران امیرکبیر, 4(2), 113-122. doi: 10.22060/ajmc.2022.21712.1102
Somayeh Shaban; Mehdi Nadjafikhah. "Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations". نشریه مهندسی عمران امیرکبیر, 4, 2, 1401, 113-122. doi: 10.22060/ajmc.2022.21712.1102
Shaban, Somayeh, Nadjafikhah, Mehdi. (1401). 'Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations', نشریه مهندسی عمران امیرکبیر, 4(2), pp. 113-122. doi: 10.22060/ajmc.2022.21712.1102
Shaban, Somayeh, Nadjafikhah, Mehdi. Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations. نشریه مهندسی عمران امیرکبیر, 1401; 4(2): 113-122. doi: 10.22060/ajmc.2022.21712.1102

Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations

AUT Journal of Mathematics and Computing
مقاله 2، دوره 4، شماره 2، 2023، صفحه 113-122    اصل مقاله (427.09 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21712.1102
نویسندگان
Somayeh Shaban1؛ Mehdi Nadjafikhah* 2
1Department of Mathematics, Karaj branch, Islamic Azad University, Karaj, Iran
2Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
چکیده
This work is intended to compute the $\mu$-symmetry and $\mu$-conservation laws for the Cammasa-Holm (CH) equation and the Hunter-Saxton (HS) equation. In other words, $\mu$-symmetry, $\mu$-symmetry reduction, variational problem, and $\mu$-conservation laws for the CH equation and the HS equation are provided. Since the CH equation and the HS equation are of odd order, they do not admit a variational problem. First we obtain $\mu$-conservation laws for both of them in potential form because they admit a variational problem and then using them, we obtain $\mu$-conservation laws for the CH equation and the HS equation.
کلیدواژه‌ها
Symmetry؛ $\mu$-Symmetry؛ Conservation law؛ $\mu$-Conservation law؛ Variational problem؛ Order reduction
مراجع
  1. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), pp. 1661–1664.
  2. Cicogna and G. Gaeta, Noether theorem for µ-symmetries, J. Phys. A, 40 (2007), pp. 11899–11921.
  3. Gaeta and P. Morando, On the geometry of lambda-symmetries and PDE reduction, J. Phys. A, 37 (2004), pp. 6955–6975.
  4. K. Hunter and R. Saxton, Dynamics of director fields, SIAM J. Appl. Math., 51 (1991), pp. 1498–1521.
  5. K. Hunter and Y. X. Zheng, On a completely integrable nonlinear hyperbolic variational equation, Phys. D, 79 (1994), pp. 361–386.
  6. Muriel and J. L. Romero, New methods of reduction for ordinary differential equations, IMA J. Appl. Math., 66 (2001), pp. 111–125.
  7. , C∞-symmetries and reduction of equations without Lie point symmetries, J. Lie Theory, 13 (2003), pp. 167–188.
  8. Muriel, J. L. Romero, and P. J. Olver, Variational C∞-symmetries and Euler-Lagrange equations, J. Differential Equations, 222 (2006), pp. 164–184.
  9. Nadjafikhah and F. Ahangari, Symmetry analysis and conservation laws for the Hunter-Saxton equation, Commun. Theor. Phys. (Beijing), 59 (2013), pp. 335–348.
  10. Nadjafikhah and V. Shirvani-Sh, Symmetry classification and conservation laws for higher order camassa-holm equation, 2011.
  11. J. Olver, Applications of Lie groups to differential equations, vol. 107 of Graduate Texts in Mathematics, Springer-Verlag, New York, second ed., 1993.
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