Conservation Laws in Thomas's Model of Ion Exchange in a Heterogeneous Solution

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Authors

  • N.H. Ibragimov Laboratory “Group analysis of mathematical models in natural and engineering sciences”, Ufa StateAviation Technical University, 450 000 Ufa, Russia Author
  • Raisa Khamitova Department ofMathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden Author

DOI:

https://doi.org/10.5890/DNC.2013.04.004

Abstract

Physically significant question on calculation of conservation laws of the Thomas equation is investigated. It is demonstrated that the Thomas equation is nonlinearly self-adjoint. Using this property and applying the theorem on nonlocal conservation laws the infinite set of conservation laws corresponding to the symmetries of the Thomas equation is computed. It is shown that the Noether theorem provides only one of these conservation laws.

References

[1] Thomas, H.C. (1944), Heterogeneous ion exchange in a flowing system, Journal of the American Chemical Society 66, 1664-1666.

[2] Rosales, R.R. (1978), Exact solutions of some nonlinear evolution equations, Studies in Applied Mathematics 59, 117-151.

[3] Wei, G.M., Gao, Y.T., and Zhang, H. (2002), On the Thomas equation for the ion-exchange operations, Czechoslovak Journal of Physics, 52 (6), 749-751.

[4] Yan, Z.Y. (2003), Study of the Thomas equation: a more general transformation (auto-Bäcklund tarnsformation) and exact solutions, Czechoslovak Journal of Physics, 53 (4), 297-300.

[5] Ibragimov, N.H. (2011), Nonlinear self-adjointness and conservation laws, Journal of Physics A: Mathematical and Theoretical 44, 432002.

[6] Ibragimov, N.H. (2011), Nonlinear self-adjointness in constructing conservation laws, arXiv:1109.1728v1[mathph] 1-104. See also Archives of ALGA 7/8 (2010-2011), 1-99.

[7] N.H. Ibragimov and R. Khamitova, Nonlinear self-adjointness and conservation laws of the Thomas equation, Archives of ALGA 7/8 (2010-2011), 147-159.

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PublishedApril 2013

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Issue

Vol. 2 No. 2 (2013): Regular Issue

Section

Research Articles

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How to Cite

Ibragimov, N., & Khamitova, R. (2026). Conservation Laws in Thomas’s Model of Ion Exchange in a Heterogeneous Solution. Discontinuity, Nonlinearity, and Complexity, 2(2), 147-158. https://doi.org/10.5890/DNC.2013.04.004

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