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DERIVATION AND SOLITON DYNAMICS OF A NEW NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT SYSTEM

ABSTRACT
Under investigation in this paper is a new and more general non-isospectral and variable-coefficient non-linear integrodifferential system. Such a system is Lax integrable because of its derivation from the compatibility condition of a generalized linear non-isospectral problem and its accompanied time evolution equation which is generalized in this paper by embedding four arbitrary smooth enough functions. Soliton solutions of the derived system are obtained in the framework of the inverse scattering transform method with a time-varying spectral parameter. It is graphically shown the dynamical evolutions of the obtained soliton solutions possess time-varying amplitudes and that the inelastic collisions can happen between two-soliton solutions.
KEYWORDS
PAPER SUBMITTED: 2018-05-10
PAPER REVISED: 2018-09-02
PAPER ACCEPTED: 2018-11-01
PUBLISHED ONLINE: 2019-03-31
DOI REFERENCE: https://doi.org/10.2298/TSCI180510076X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S639 - S646]
REFERENCES
  1. Russell Scott, J., Report on Waves, Fourteen meeting of the British association for the advancement of science, John Murray, London, 1844.
  2. Chen, D. Y., Introduction of Soliton (in Chinese), Science Press, Beijing, China, 2006
  3. Ablowitz, M. J., Clarkson, P. A., Solitons, Non-linear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991
  4. Chen, H. H., Liu, C. S., Solitons in Nonuniform Media, Physical Review Letters, 37 (1976), 11, pp. 693-697
  5. Hirota, R., Satsuma, J., N-Soliton Solutions of the K-dV Equation with Loss and Nonuniformity Terms, Journal of the Physical Society of Japan, 41 (1976), 6, pp. 2141-2142
  6. Serkin, V. N., et al., Nonautonomous solitons in external potentials, Physical Review Letters, 98 (2007), 7, ID 074102
  7. Zhang, S., et al., Exact Solutions of a KdV Equation Hierarchy with Variable Coefficients, International Journal of Computer Mathematics, 91 (2014), 7, pp. 1601-1616
  8. Zhang, S., Gao, X. D., Exact Solutions and Dynamics of Generalized AKNS Equations Associated with the Non-Isospectral Depending on Exponential Function, Journal of Nonlinear Science and Applications, 9 (2016), 6, pp. 4529-4541
  9. Zhang, S., Li, J. H., On Non-Isospectral AKNS System with Infinite Number of Terms and its Exact Solutions, IAENG International Journal of Applied Mathematics, 47 (2017), 1, pp. 89-96
  10. Zhang, S., Li, J. H., Soliton Solutions and Dynamical Evolutions of a Generalized AKNS System in the Framework of Inverse Scattering Transform, Optik, 137 (2017), 1, pp. 228-237
  11. Zhang, S., Hong, S. Y., Lax Integrability and Soliton Solutions for a Non-Isospectral Integrodifferential System, Complexity, 2017, ID 9457078
  12. Zhang, S., Hong, S. Y., Lax Integrability and Exact Solutions of a Variable-Coefficient and Non-Isospectral AKNS Hierarchy, International Journal of Nonlinear Sciences and Numerical Simulation, 2017, doi: 10.1515/ijnsns-2016-0191
  13. Zhang, S., Wang, D., Variable-Coefficient Non-Isospectral Toda Lattice Hierarchy and its Exact Solutions, Pramana-Journal of Physics, 85 (2015), 6, pp. 1143-1156
  14. Fujioka, J., et al., Fractional Optical Solitons, Physics Letters A, 374 (2010), 9, pp. 1126-1134
  15. Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 8, ID 084312
  16. Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers-Type Equations, Computers and Mathematics with Applications, 73 (2017), 2, 203-210
  17. Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), Sep., pp.285-296
  18. Yang, X. J., et al., Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation, Abstract and Applied Analysis, 2014, ID 278672

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