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The Broer-Kaup equation is one of many equations describing some phenomena of shallow water wave. There are many errors in scientific research because of the existence of the non-smooth boundaries. In this paper, we generalize the Broer-Kaup equation to the fractal space and establish fractal variational formulations through the semi-inverse method. The acquired fractal variational formulation reveals conservation laws in an energy form in the fractal space and suggests possible solution structures of the morphology of the solitary waves
PAPER REVISED: 2018-06-20
PAPER ACCEPTED: 2018-06-28
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THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2051 - 2056]
  1. Wu, P. X., Zhang, Y. F., Lump, Lumpoff and Predictable Rogue Wave Solutions to the (2+1)- Dimensional Asymmetrical Nizhnik-Novikov-Veselov Equation, Physics Letters A, 383 (2019), 15, pp. 1755-1763
  2. Wu, P. X., et al., Lump, Periodic Lump and Interaction Lump Stripe Solutions to the (2+1)-Dimensional B-Type Kadomtsev-Petviashvili Equation, Modern Physics Letters B, 32 (2018), 7, ID 1850106
  3. Broer, L. J. F., Approximate Equations for Long Water Waves, Applied Scientific Research, 31 (1975), 5, pp. 377-395
  4. Kaup, D. J., A Higher-Order Water-Wave Equation and the Method for Solving It, Progress of Theoretical Physics, 54 (1975), 2, pp. 396-408
  5. Kupershmidt, B. A., Mathematics of Dispersive Water Waves, Communications in Mathematical Physics, 99 (1985), 1, pp. 51-73
  6. Chavchanidze, G., Non-Noether Symmetries in Hamiltonian Dynamical Systems, Mem. Differential Equations Math. Phys, 36 (2004), June, pp. 81-134
  7. Zhou, Z. J., Li, Z. B., A Darboux Transformation and New Exact Solutions for Broer-Kaup System, Chinese Physics, 52 (2003), 2, pp. 262-266
  8. Satsuma, J., et al., Solutions of the Broer-Kaup System Through its Trilinear Form, Journal of the Physical Society of Japan, 61 (1992), 9, pp. 3096-3102
  9. Svinin, A. K., Differential Constraints for the Kaup-Broer System as a Reduction of the 1D Toda Lattice, Inverse Problems, 17 (2001), 4, pp. 1061-1066
  10. Zhang, S., Xia, T., A Generalized F-Expansion Method with Symbolic Computation Exactly Solving Broer-Kaup Equations, Applied Mathematics and Computation, 189 (2007), 1, pp. 836-843
  11. Chen, C. L., Lou, S. Y., CTE Solvability and Exact Solution to the Broer-Kaup System, Chinese Physics Letters, 30 (2013), 11, ID 110202
  12. Meng, Q., et al., Smooth and Peaked Solitary Wave Solutions of the Broer-Kaup System Using the Approach of Dynamical System, Communications in Theoretical Physics, 62 (2014), 3, pp. 308-314
  13. Jiang, B., Bi, Q. S., Peaked Periodic Wave Solutions to the Broer-Kaup Equation, Communications in Theoretical Physics, 67 (2017), 1, pp. 22-26
  14. He, J. H., Fractal Calculus and Its Geometrical Explanation, Results in Physics, 10 (2018), Sept., pp. 272-276
  15. He, J. H., A Tutorial Review on Fractal Spacetime and Fractional Calculus, International Journal of Theoretical Physics, 53 (2014), 11, pp. 3698-3718
  16. Ain, Q. T., He, J. H., On Two-Scale Dimension and Its Applications, Thermal Science, 23 (2019), 3B, pp. 1707-1712
  17. He, J. H., Ji, F. Y., Two-Scale Mathematics and Fractional Calculus For Thermodynamics, Thermal Science, 23 (2019), 4, pp. 2131-2133
  18. He, J. H., Hamilton's Principle for Dynamical Elasticity, Applied Mathematics Letters, 100 (2017), 72, pp. 65-69
  19. Wu, Y., He, J. H., A Remark on Samuelson's Variational Principle in Economics, Applied Mathematics Letters, 84 (2018), Oct., pp. 143-147
  20. Tao, Z. L., Variational Approach to the Benjamin Ono Equation, Nonlinear Analysis: Real World Applications, 10 (2009), 3, pp. 1939-1941
  21. He, J. H., Generalized Equilibrium Equations for Shell Derived from a Generalized Variational Principle, Applied Mathematics Letters, 64 (2017), Feb., pp. 94-100
  22. Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, ID 1950047
  23. He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-2081
  24. He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, Journal of Applied and Computational Mechanics, 6 (2019), 4, pp. 735-740
  25. He, J. H., Variational Principles for Some Nonlinear Partial Differential Equations with Variable Coefficients, Chaos, Solitons & Fractals, 19 (2004), 4, pp. 847-851
  26. He, J. H., A Fractal Variational Theory for One-Dimensional Compressible Flow in a Microgravity Space, Fractals, 28 (2020), 2, ID 2050024
  27. Wang, K. L., He, C, H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID, 1950134

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