THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Hong-Cai Ma

,

Ke Ni

,

Guo-Ding Ruan

,

Ai-Ping Deng

RATIONAL SOLUTION TO A SHALLOW WATER WAVE-LIKE EQUATION

ABSTRACT
Two classes of rational solutions to a shallow water wave-like non-linear differential equation are constructed. The basic object is a generalized bilinear differential equation based on a prime number, p = 3. Through this new transformation and with the help of symbolic computation with MAPLE, both the new equation and its rational solutions are obtained.
KEYWORDS
rational solution, generalized bilinear equation, shallow water wave-like equation
PAPER SUBMITTED: 2015-11-01
PAPER REVISED: 2015-12-10
PAPER ACCEPTED: 2016-02-01
PUBLISHED ONLINE: 2016-08-13
DOI REFERENCE: https://doi.org/10.2298/TSCI1603875M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 3, PAGES [875 - 880]
REFERENCES
  1. Zhang, Y., Ma, W. X., Rational Solutions to a KdV-like Equation, Applied Mathematics and Computation, 256 (2015), 1, pp. 252-256
  2. Ma, W. X., Trilinear Equations, Bell Polynomials, and Resonant Solutions, Frontiers of Mathematics in China, 8 (2013), 5, pp. 1139-1156
  3. Ma, W. X., Lump Solutions to the Kadomtsev-Petviashvili Equation, Physics Letters A, 379 (2015), 36, pp. 1975-1978
  4. Ma, W. X., You, Y., Solving the Korteweg-de Vries Equation by its Bilinear Form: Wronskian Solutions, Transactions of the American Mathematical Society, 357 (2005), 5, pp. 1753-1778
  5. He, J.-H., Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  6. Ma, H. C., et al., Lie Symmetry and Exact Solution of (2+1)-Dimensional Generalized KP Equation with Variable Coefficients, Thermal Science, 17 (2013), 5, pp. 1490-1493
  7. Ma, H. C., et al., Exact Solutions of Non-Linear Fractional Partial Differential Equations by Fractional Sub-Equation Method, Thermal Science, 19 (2015), 4, pp. 1239-1244
  8. Hu, X. B., Wu, Y. T., Application of the Hirota Bilinear Formalism to a New Integrable Differential-Difference Equation, Physics Letters A, 246 (1998), 6, pp. 523-529
  9. Wang, X., et al., Generalized Darboux Transformation and Localized Waves in Coupled Hirota Equations, Wave Motion, 51 (2014), 7, pp. 1149-1160
  10. Elwakil, S. A., et al., Exact Travelling Wave Solutions for the Generalized Shallow Water Wave Equation, Chaos, Solitons & Fractals, 17 (2003), 1, pp. 121-126
  11. Ma, W. X., You, Y., Rational Solutions of the Toda Lattice Equation in Casoratian form, Chaos Solitons & Fractals, 22 (2004), 2, pp. 395-406
  12. Hietarinta, J., A Search for Bilinear Equations Passing Hirota's Three-Soliton Condition. IV. Complex Bilinear Equations, Journal of Mathematical Physics, 29 (1988), 3, pp. 628-635
  13. Wadati, M., Introduction to Solitons, Pramana, 57 (2001), 5-6, pp. 841-847
  14. Bagchi, B., et al., New Exact Solutions of a Generalized Shallow Water Wave Equation, Physica Scripta, 82 (2010), 2, pp. 1485-1502
  15. Hirota, R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, UK, 2004
  16. Thacker, W. C., Some Ex act Solutions to the Nonlinear Shallow-Water Wave Equations, Journal of Fluid Mechanics, 107 (1981), 6, pp. 499-508
  17. Free man, N. C., Nimmo, J. J. C., Soliton Solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili Equations: The Wronskian Technique, Physics Letters A, 95 (1983), 1, pp. 1-3
  18. Zhang, H., New Exact Travelling Wave Solutions for Some Nonlinear Evolution Equations, Chaos Solitons & Fractals, 26 (2005), 4, pp. 921-925
  19. Ma, W. X., Bilinear Equa tions, Bell Polynomials and Linear Superposition Principle, Journal of Physics Conference Series, 411 (2013), 1, pp. 594-597
  20. Ma, W. X., Generalized Bilinear Differential Equations, Studies in Nonlinear Sciences, 2 (2011), 4, pp. 140-144
PDF VERSION [DOWNLOAD]
Rational solution to a shallow water wave-like equation

© 2024 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