International Scientific Journal

Authors of this Paper

External Links


Differential-difference equations are often considered as an alternative approach to describing some phenomena arising in heat/electron conduction and flow in carbon nanotubes and nanoporous materials. Infinite many conservation laws play important role in discussing the integrability of non-linear differential equations. In this paper, infinite many conservation laws of the non-linear differential-difference equations associated with a 3×3 matrix spectral problem are obtained.
PAPER REVISED: 2016-10-15
PAPER ACCEPTED: 2016-10-25
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1613 - 1619]
  1. Zhang, D. J., Chen, D. Y., The Conservation Laws of Some Discrete Soliton Systems, Chaos, Solitons and Fractals, 14 (2002), 4, pp. 573-579
  2. Miura, R. M., et al., KdV Equation and Generalizations, II. Existence of Conservation Laws and Con-stants of Motion, Journal of Mathematical Physics, 9 (1968), 8, pp. 1204-1209
  3. Ablowitz, M. J., et al., A Note on Miura's Transformation, Journal of Mathematical Physics, 20 (1974), 6, pp. 999-1003
  4. Kruskal, M. D., et al. Korteweg-de Vries Equation and Generalizations: V. Uniqueness and Non-Existence of Polynomial Conservation Laws, Journal of Mathematical Physics, 11 (1970), 3, pp. 952-960
  5. Tu, G. Z., Qin, M. Z., The Invariant Groups and Conservation Laws of Non-linear Evolution Equations -An Approach of Symmetric Function, Science China Mathematics, 24 (1981), 1, pp. 13-26
  6. Wen, X. Y., A New Integrable Lattice Hierarchy Associated with a Discrete 3×3 Matrix Spectral Prob-lem: N-Fold Darboux Transformation and Explicit Solutions, Reports on Mathematical Physics, 71 (2013), 1, pp. 15-32
  7. Zhang, S., et al., Differential-Difference Equation Arising in Nanotechnology and it's Exact Solutions, Journal of Nano Research, 23 (2013), 1, pp. 113-116
  8. He, J.-H., Zhu, S. D., Differential-Difference Model for Nanotechnology, Journal of Physics: Confer-ence Series, 96 (2008), 1,
  9. Hu, Y., He, J.-H., On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777
  10. Zhang, S., et al., Variable Separation for Time Fractional Advection-Dispersion Equation with Initial and Boundary Conditions, Thermal Science, 20 (2016), 3, pp. 789-792
  11. Zhang, S., et al., Exact Solutions of Time Fractional Heat-Like and Wave-Like Equations with Variable Coefficients, Thermal Science, 20 (2016), Suppl. 3, pp. S689-S693
  12. Zhang, S., Zhang, H. Q., Fractional Sub-Equation Method and its Applications to Non-Linear Fractional PDEs, Physics Letters A, 375 (2011), 7, pp. 1069-1073
  13. Wang, K. L., Liu, S. Y., He's Fractional Derivative for Non-Linear Fractional Heat Transfer Equation, Thermal Science, 20 (2016), 3, pp. 793-796
  14. Zhang, S., et al., Exact Solutions of a KdV Equation Hierarchy with Variable Coefficients, International Journal of Computer Mathematics, 91 (2014), 7, pp. 1601-1616
  15. Zhang, S., Wang, D., A Toda Lattice Hierarchy with Variable Coefficients and its Multi-Wave Solu-tions, Thermal Science, 18 (2014), 5, pp. 1555-1558
  16. Zhang, S., Cai, B., Multi-Soliton Solutions of a Variable-Coefficient KdV Hierarchy, Nonlinear Dynam-ics, 78 (2014), 3, pp. 1593-1600
  17. Ning, T. K., et al., The Exact Solutions for the Non-Isospectral AKNS Hierarchy through the Inverse Scattering Transform, Physica A Statistical Mechanics & Its Applications, 339 (2007), 3-4, pp. 248-266
  18. Zhang, S., Wang, D., Variable-Coefficient Non-Isospectral Toda Lattice Hierarchy and its Exact Solu-tions, Pramana-Journal of Physics, 86 (2016), 6, pp. 1259-1267
  19. Zhang, S. Zhang, L. Y., Bilinearization and New Multi-Soliton Solutions of MKdV Hierarchy with Time-Dependent Coefficients, Open Physics, 14 (2016), 1, pp. 69-75
  20. Wang, J., Hu, Y., On Chain Rule in Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 803-806

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence