THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ANALYTICAL TREATMENT ON A NEW GENERALIZED ABLOWITZ-KAUP-NEWELL-SEGUR HIERARCHY OF THERMAL AND FLUID EQUATIONS

ABSTRACT
Constructing analytical solutions for non-liner partial differential equations aris-ing in thermal and fluid science is important and interesting. In this paper, Hiro-ta's bi-linear method is extended to a new generalized Ablowitz-Kaup-Newell-Se-gur hierarchy which includes heat conduction equation, advection equation, ad-vection-dispersion equation, and Korteweg-de Vries equation as special cases. As a result, bi-linear form of the generalized Ablowitz-Kaup-Newell-Segur hierarchy is derived. Based on the derived bi-linear form, exact and explicit n-soliton solu-tions of the generalized Ablowitz-Kaup-Newell-Segur hierarchy are obtained.
KEYWORDS
PAPER SUBMITTED: 2016-06-23
PAPER REVISED: 2016-10-15
PAPER ACCEPTED: 2016-10-25
PUBLISHED ONLINE: 2017-09-09
DOI REFERENCE: https://doi.org/10.2298/TSCI160623042Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 4, PAGES [1607 - 1612]
REFERENCES
  1. Gardner, C. S., et al., Method for Solving the Korteweg-de Vries Equation, Physical Review Letters, 19 (1967), 19, pp. 1095-1197
  2. Hirota, R., Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons, Phys-ics Review Letters, 27 (1971), 18, pp. 1192-1194
  3. Wang, M. L., Exact Solutions for a Compound KdV-Burgers Equation, Physics Letters A, 213 (1996), 5-6, pp. 279-287
  4. He, J. H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos, Solitons & Frac-tals, 30 (2006), 3, pp. 700-708
  5. Zhang, S., Xia, T. C., A Generalized Auxiliary Equation Method and Its Application to (2+1)-Dimen-sional Asymmetric Nizhnik-Novikov-Vesselov Equations, Journal of Physics A: Mathematical and The-oretical, 40 (2006), 2, pp. 227-248
  6. Zhang, S., Xia, T. C., A Generalized F-Expansion Method and New Exact Solutions of Konopelchenko- -Dubrovsky Equations, Applied Mathematics and Computation, 183 (2006), 3, pp. 1190-1200
  7. Zhang, S., et al., A Generalized (G'/G)-Expansion Method for the MKdV Equation with Variable Coef-ficients, Physics Letters A, 372 (2008), 13, pp. 2254-2257
  8. Zhang, S., Zhang, H. Q., Fractional Sub-Equation Method and Its Applications to Non-Linear Fractional PDE, Physics Letters A, 375 (2011), 7, pp. 1069-1073
  9. Zhang, S., Xia, T. C., Variable-Coefficient Jacobi Elliptic Function Expansion Method for (2+1)- -Dimensional Nizhnik-Novikov-Vesselov Equations, Applied Mathematics and Computation, 218 (2011), 4, pp. 1308-1316
  10. Zhang S., et al., Painleve Analysis for a Forced Korteveg-de Vries Equation Arisen in Fluid Dynamics of Internal Solitary Waves, Thermal Science, 19 (2015), 4, pp. 1223-1226
  11. 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
  12. Chen, D. Y., Introduction to Soliton (in Chinese), Science Press, Beijing, 2006
  13. Zhang, S., Gao, X. D., Exact N-Soliton Solutions and Dynamics of a New AKNS Equations with Time-Dependent Coefficients, Nonlinear Dynamics, 83 (2016), 1, pp. 1043-1052

© 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