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In this paper, the simplest exp-function method which combines the exp-function method with a direct algorithm is used to exactly solve the Mikhauilov-Novikov-Wang equations. As a result, two explicit and exact solutions are obtained. It is shown that the simplest exp-function method provides a simpler but more effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.
PAPER REVISED: 2018-11-23
PAPER ACCEPTED: 2018-11-23
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THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2381 - 2388]
  1. He, J.-H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos, Solitons and Fractals, 30 (2006), 3, pp. 700-708
  2. He, J.-H., Abdou, M. A., New Periodic Solutions for Non-Linear Evolution Equations Using Exp-Function Method, Chaos, Solitons and Fractals, 34 (2006), 5, pp. 1421-1429
  3. He, J.-H., Exp-Function Method for Fractional Differential Equations, Journal of Non-Linear Sciences and Numerical Simulation, 14 (2013), 6, pp. 363-366
  4. Ebaid, A., Exact Solitary Wave Solutions for Some Non-Linear Evolution Equations via Exp-Function Method, Physics Letters A, 365 (2007), 3, pp. 213-219
  5. Zhang, S., Application of Exp-Function Method to a KdV Equation with Variable Coefficients, Physics Letters A, 365 (2007), 5-6, 448-453
  6. Zhang S., Application of Exp-Function Method to High-Dimensional Non-Linear Evolution Equation, Chaos, Solitons and Fractals, 38 (2008), 1, pp. 270-276
  7. Zhang, S., Zhang, H. Q., An Exp-Function Method for New N-soliton Solutions with Arbitrary Functions of a (2+1)-Dimensional vcBK System, Computers and Mathematics with Applications, 61 (2011), 8, pp. 1923-1930
  8. Zhang, S., et al., Multi-Wave Solutions for a Non-Isospectral KdV-Type Equation with Variable Coefficients, Thermal Science, 16 (2012), 5, pp. 1576-1579
  9. 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
  10. Shan, X. Y., Zhu. J. Y., The Mikhauilov-Novikov-Wang Hierarchy and its Hamiltonian Structures, Acta Physica Polonica B, 43 (2012), 10, 1953-1963
  11. Zhang, S., Zhang, L. Y., New Periodic Wave Solutions for MNW Hierarchy with the Aid of Computer-ized Symbolic Computation, Advances in Computer Science Research, 71 (2017), 1, pp. 1233-1237
  12. Zhang, S., Tian, C., A New Mathematical Model and its Solvability Test on Computer, Advances in En-gineering Research, 97 (2016), 1, pp. 375-379
  13. 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
  14. 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
  15. Wang, J., Hu, Y., On Chain Rule in Fractional Calculus, Thermal Science, 20, (2016), 3, pp. 803-806
  16. Yang, X. J., Fractional Derivatives of Constant and Variable Orders Applied to Anomalous Relaxation Models in Heat-Transfer Problems, Thermal Science, 21 (2017), 3, pp. 1161-1171
  17. Zhang, S., Hong, S. Y., Variable Separation Method for a Non-Linear Time Fractional Partial Differen-tial Equation with Forcing Term, Journal of Computational and Applied Mathematics, 339 (2018), 1, pp. 297-305
  18. 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
  19. He, J.-H. A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  20. He, J.-H. Fractal Calculus and its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  21. Wang, Y., An, J. Y., Amplitude-Frequency Relationship to a Fractional Duffing Oscillator Arising in Microphysics and Tsunami Motion, Journal of Low Frequency Noise, Vibration & Active Control, On-line first,
  22. 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
  23. Wang, Q. L., et al., Fractal Calculus and its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, ID 1850086
  24. Wang, Y., Deng, Q. G., Fractal Derivative Model for Tsunami Travelling, Fractals, 27 (2019), 2, ID 1950017
  25. Hu, Y., He, J.-H, On Fractal Space-Time and Fractional Calculus, Thermal Science, 20 (2016), 3, pp. 773-777

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