THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Jiangen Liu

,

Pinxia Wu

,

Yufeng Zhang

,

Lubin Feng

NEW PERIODIC WAVE SOLUTIONS OF (3+1)-DIMENSIONAL SOLITON EQUATION

ABSTRACT
In this paper, associating with the Hirota bilinear form, the three-wave method, which is applied to construct some periodic wave solutions of (3+1)-dimensional soliton equation, is a powerful approach to obtain periodic solutions for many non-linear evolution equations in the integrable systems theory.
KEYWORDS
periodic wave solutions, three-wave method, Hirota bilinear form, (3+1)-dimensional soliton equation
PAPER SUBMITTED: 2017-03-01
PAPER REVISED: 2017-05-01
PAPER ACCEPTED: 2017-05-20
PUBLISHED ONLINE: 2017-12-02
DOI REFERENCE: https://doi.org/10.2298/TSCI17S1169L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Supplement 1, PAGES [S169 - S176]
REFERENCES
  1. Drazin, P. G., Johnson, R. S., Solitons: An Introduction, Cambridge University Press, Cambridge, USA, 1989
  2. Gardner, C. S., et al., Method for Solving the Korteweg-de Vries Equation, Physical Review Letters, 19 (1967), 19, pp. 1095-1197
  3. Xia, B., et al., Darboux Transformation and Multi-Soliton Solutions of the Camassa-Holm Equation and Modified Camassa-Holm Equation, Journal of Mathematical Physics, 57 (2016), 10, pp. 1661-1664
  4. Dong, H., et al., The New Integrable Symplectic Map and the Symmetry of Integrable Nonlinear Lattice Equation, Communications in Nonlinear Science & Numerical Simulation, 36 (2016), 2, pp. 354-365
  5. Dong, H., et al., Generalised (2+1)-Dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory, East Asian Journal on Applied Mathematics, 5 (2015), 3, pp. 256-272
  6. Dong, H. H., et al. Generalized Fractional Supertrace Identity for Hamiltonian Structure of NLS-MKdV Hierarchy with Self-Consistent Sources, Analysis and Mathematical Physics, 6 (2016), 2, pp. 199-209
  7. Yang, X. J., et al., Nonlinear Dynamics for Local Fractional Burgers' Equation Arising in Fractal Flow, Nonlinear Dynamics, 84 (2015), 1, pp. 3-7
  8. Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos,26 (2016), 8, pp. 110-118
  9. Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers Type Equations, Computers &Mathematics with applications, 73 (2017), 2, pp. 203-210
  10. Zhang, Y. F., Wang, Y., Generating Integrable Lattice Hierarchies by Some Matrix and Operator Lie Algebras, Advances in Difference Equations, 2016 (2016), 1, pp. 313
  11. Zhang, Y., Ma, W. X., Rational Solutions to a KdV-Like Equation, Applied Mathematics & Computation, 256 (2015), C, pp. 252-256
  12. Zhang, Y. F., Ma, W. X., A Study on Rational Solutions to a KP-like Eqation, Zeitschrift Fuer Naturf-Orschung, 70 (2015), A, pp. 263 -268
  13. Lax, P. D., Periodic Solutions of the KdV Equation, Siam Review, 18 (2004), 3, pp. 438-462
  14. Liu, J., et al., Spatiotemporal Deformation of Multi-Soliton to (2+1)-Dimensional KdV Equation, Nonlinear Dynamics, 83 (2016), 1-2, pp. 355-360
  15. Hirota, R., Reduction of Soliton Equations in Bilinear Form, Physica D Nonlinear Phenomena, 18 (1986), s-13, pp. 161-170
  16. Wang, J. M., Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation, Chinese Physics Letters, 29 (2012), 2, pp. 20203-20206
  17. Geng, X., Ma, Y., N-Soliton Solution and its Wronskian Form of a (3+1)-Dimensional Nonlinear Evolution Equation, Physics Letters A, 369 (2007), 4, pp. 285-289
  18. Wu, J. P., Grammian Determinant Solution and Pfaffianization for a (3+1)-Dimensional Soliton Equation, Communications in Theoretical Physics, 52 (2009), 11, pp. 791-794
  19. Hirota, R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, Mass., USA, 2004
  20. Ma, W. X., Fan, E. G., Linear Superposition Principle Applying to Hirota Bilinear Equations, Co-Mput. Math. Appl., 61 (2011), 4, pp. 950-959
  21. Wu, J. P., A Bilinear B Cklund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation, Chinese Physics Letters, 25 (2008), 12, pp. 4192-4194
  22. Qu, Y. D., et al., Acta Phys. Sin., Acta Physica Sinica, 61 (2012), 3 pp. 69701-069701
  23. Ma, W. X., Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials, Reports on Mathematical Physics, 72 (2013), 1, pp. 41-56
  24. Gilson, C, et al., On the Combinatorics of the Hirota D-Operators, Proceedings of the Royal Society A Mathematical Physical & Engineering Sciences, 452 (1996), 452, pp. 223-234
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New periodic wave solutions of (3+1)-dimensional soliton equation

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