THERMAL SCIENCE

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Sheng Zhang

,

Mei-Tong Chen

,

Wei-Yi Qian

PAINLEVE ANALYSIS FOR A FORCED KORTEVEG-DE VRIES EQUATION ARISEN IN FLUID DYNAMICS OF INTERNAL SOLITARY WAVES

ABSTRACT
In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.
KEYWORDS
Painleve analysis, forced Korteveg-de Vries equation, exact solution, Weiss-Tabor-Carnevale method
PAPER SUBMITTED: 2015-01-10
PAPER REVISED: 2015-03-05
PAPER ACCEPTED: 2015-04-20
PUBLISHED ONLINE: 2015-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI1504223Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 4, PAGES [1223 - 1223]
REFERENCES
  1. Grimshaw, R., et al., Modelling Internal Solitary Waves in the Coastal Ocean, Surveys in Geophysics, 28 (2007), 4, pp. 273-289
  2. Lamb, K. G., et al., Breather Generation in Fully non-Linear Models of a Stratified Fluid, Physical review E, 75 (2007), 4, 046306
  3. Liu, Y., et al., Multi-Soliton Solutions of the Forced Variable-Coefficient Extended Korteweg-de Vries Equation Arisen in Fluid Dynamics of Internal Solitary Waves, Non-linear Dynamics, 66 (2011), 4, pp. 575-587
  4. Ablowitz, M. J., Clarkson, P. A., Solitons, Non-Linear Evolution Equations and Inverse Scattering, Cambridge University Press, New York, USA, 1991
  5. Hirota, R., Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons, Physics Review Letters, 27 (1971), 18, pp. 1192-1194
  6. Chen, D. Y., Introduction to Soliton (in Chinese), Science Press, Beijing, China, 2006
  7. 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
  8. Zhang, S., Wang, D., A Toda Lattice Hierarchy with Variable Coefficients and Its Multi-Wave Solutions, Thermal Science, 18 (2014), 5, pp. 1555-1558
  9. Weiss, J., et al., The Painleve Property for Partial Differential Equations, Journal of Mathematical Physics, 24, (1983), 3, pp. 522-526
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PAINLEVE ANALYSIS FOR A FORCED KORTEVEG-DE VRIES EQUATION ARISEN IN FLUID DYNAMICS OF INTERNAL SOLITARY WAVES

© 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