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DARBOUX TRANSFORM AND CONSERVATION LAWS OF NEW DIFFERENTIAL-DIFFERENCE EQUATIONS

ABSTRACT
Darboux transforms, exact solutions and conservation laws are important topics in thermal science and other fields as well. In this paper, the new non-linear differential-difference equations associated a discrete linear spectral problem are studied analytically. Firstly, the Darboux transform of the studied equations is constructed, and exact solutions are then obtained. Finally, infinite many conservation laws are derived.
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PAPER SUBMITTED: 2019-04-28
PAPER REVISED: 2019-08-10
PAPER ACCEPTED: 2019-09-08
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004519Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 4, PAGES [2519 - 2527]
REFERENCES
  1. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  2. He, J. H., Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  3. Li, X. X., et al., A Fractal Modification of the Surface Coverage Model for an Electrochemical Arsenic Sensor, Electrochimica Acta, 296 (2019), Feb., pp. 491-493
  4. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, 1850086
  5. Wang, Y., Deng, Q., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 1, 1950017
  6. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus for Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  7. Ain, Q. T., He, J. H., On Two-Scale Dimension and its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  8. He, J. H., Zhu, S. D., Differential-Difference Model for Nanotechnology, Journal of Physics: Conference Series, 96 (2008), 1, ID 012189
  9. Zhang, S., et al., Differential-Difference Equation Arising in Nanotechnology and its Exact Solutions, Journal of Nano Research, 23 (2013), 1, pp. 113-116
  10. Zhang, S., Liu, D. D., Infinite Many Conservation Laws of Discrete System Associated with a 3×3 Matrix Spectral Problem, Thermal Science, 21 (2017), 4, pp. 1613-1619
  11. He, J. H., A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Meth-ods for Heat and Fluid Flow, On-line first, doi.org/10.1108/HFF-06-2019-0523, 2019
  12. He, J. H., Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, doi.org/10.1108/HFF-07-2019-0577, 2019
  13. He, J. H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos, Solitons and Fractals, 30 (2006), 3, pp. 700-708
  14. Zhang, S., et al., A Direct Algorithm of Exp-Function Method for Non-Linear Evolution Equations in Fluids, Thermal Science, 20 (2016), 3, pp. 881-884
  15. Anjum, N., He, J. H., Laplace Transform: Making the Variational Iteration Method Easier, Applied Mathematics Letters, 92 (2019), June, pp. 134-138
  16. He, J. H., Some Asymptotic Methods for Strongly Nonlinear Equations, International Journal of Modern Physics B, 20 (2006), 10, pp. 1141-1199
  17. Wu, Y., He, J. H., Homotopy Perturbation Method for Nonlinear Oscillators with Coordinate Dependent Mass., Results in Physics, 10 (2018), Sept., pp. 270-271
  18. Wu, Y., He, J. H., A Remark on Samuelson's Variational Principle in Economics, Applied Mathematics Letters, 84 (2018), Oct., pp. 143-147
  19. He, J. H., Hamilton's Principle for Dynamical Elasticity, Applied Mathematics Letters, 72 (2017), Oct., pp. 65-69
  20. He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934
  21. He, J. H., The Simplest Approach to Nonlinear Oscillators, Results in Physics, 15 (2019), Dec., ID 102546
  22. Matveev, V. B., Salle, M. A., Darboux Transformation and Solitons, Springer-Verlag: Berlin, Germany, 1991
  23. Tian, Y., Symmetry Reduction a Promising Method for Heat Conduction Equations, Thermal Science, 23 (2019 ), 4, pp. 2219-2227
  24. Tian, Y., Diffusion-Convection Equations and Classical Symmetry Classification, Thermal Science, 23 (2019), 4, pp. 2151-2156
  25. Bai, Y. S., Zhang, Q., Perturbed Korteweg-de Vries Equations Symmetry Analysis and Conservation Laws, Thermal Science, 23 (2019), 4, pp. 2281-2289
  26. Xu, X. X., A Family of Integrable Differential-Difference Equations, its Bi-Hamiltonian Structure and Binary Nonlinearization of the Lax Pairs and Adjoint Lax Pairs, Chaos, Solitons & Fractals, 45 (2012), 4, pp. 444-453

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