THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Han-Lin Chen

,

Zhen-Hui Xu

,

Zheng-De Dai

KINK DEGENERACY AND ROGUE POTENTIAL FLOW FOR THE (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

ABSTRACT
The breather-type kink soliton, breather-type periodic soliton solutions and rogue potential flow for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are obtained by using the extended homoclinic test technique and homoclinic breather limit method, respectively. Furthermore, some new non-linear phenomena, such as kink and periodic degeneracy, are investigated and the new rational breather solutions are found out. Meanwhile, we also obtained the rational potential solution and it is just a rogue wave. These results enrich the variety of the dynamics of higher-dimensional non-linear wave field.
KEYWORDS
generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, homoclinic breather limit method, rational breather solutions, kink degeneracy, rogue potential flow
PAPER SUBMITTED: 2016-03-01
PAPER REVISED: 2016-04-13
PAPER ACCEPTED: 2016-04-20
PUBLISHED ONLINE: 2016-09-24
DOI REFERENCE: https://doi.org/10.2298/TSCI16S3919C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Supplement 3, PAGES [S919 - S927]
REFERENCES
  1. Ablowitz, M. J., et al., Solitons, Non-Linear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, UK, 1991
  2. Vakhnenko, V. O., et al., A Backlund Transformation and the Inverse Scattering Transform Method for the Generalized Vakhnenko Equation, Chaos, Solitons & Fractals, 17 (2003), 4, pp. 683-692
  3. Zhao, X., et al., The Repeated Homogeneous Balance Method and Its Applications to Nonlinear Partial Differential Equations, Chaos, Solitons & Fractals, 28 (2006), 2, pp. 448-453
  4. Ling, L., et al., Darboux Transformation and Multi-Dark Soliton for N-Component Nonlinear Schroedinger Equations, Nonlinearity, 28 (2015), 9, pp. 3243-3261
  5. Senthilvelan, M., On the Extended Applications of Homogenous Balance Method, Applied Mathematics and Computation,123 (2001), 3, pp. 381-388
  6. Gu, C. H., et al., Darbour Transformation in Soliton Theory and Geometric Applications, Shanghai Science and Technology Press, Shanghai, China, 1999
  7. Matveev, V. B., et al., Darboux Transformation and Solitons, Springer, New York, USA, 1991
  8. Hirota, R., et al., Soliton Solutions of a Coupled KdV Equation, Physics Letter A, 85 (1981), 8-9, pp. 407-412
  9. Tam, H. W., et al., The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited, Journal of the Physical Society of Japan, 69 (2000), 1, pp. 45-52
  10. He, J.-H., Variational Approach to (2+1)-Dimensional Dispersive Long Water Equations, Physics Letter A, 335 (2005), 2, pp. 182-190
  11. Malfliet, W., et al., The Tanh Method I: Exact Solutions of Non-Linear Evolution and Wave Equations, Physica Scripta, 54 (1996), 6, pp. 569-575
  12. Fan, E. G., Extended Tanh-Function Method and its Applications to Non-Linear Equations, Physics Letter A, 277 (2000), 4, pp. 212-218
  13. Jimbo, M. T., et al., Solitons and Infinite Dimensional Lie Algebras, Publications of the Research Institute for Mathematical Sciences, 19 (1983), 3, pp. 943-1001
  14. Olver, P. J, Application of Lie Groups to Differential Equations, Springer, New York, USA, 1983
  15. Tang, X. Y., et al., Variable Separation Solutions for the (3+1)-Dimensional Jimbo-Miwa Equation, Physics Letter A, 351 (2006), 6, pp. 398-402
  16. Dai, Z., et al., Exact Cross Kink-Wave Solutions and Resonance for the Jimbo-Miwa Equation, Physics Letter A, 384 (2007), 2, pp. 285-290
  17. Zhu, Z. N., Painleve Property, Backlund Transformation, Lax Pair and Soliton-like Solution for a Variable Coefficient KP Equation, Physics Letter A, 182 (1993), 2-3, pp. 277-281
  18. You, F. C., et al., Decomposition of the Generalized KP, cKP and mKP and their Exact Solutions, Physics Letter A, 372 (2008), 18, pp. 3184-3194
  19. Wazwaz, A. M., Four (2+1)-Dimensional Integrable Extensions of the Kadomtsev-Petviashvili Equation, Applied Mathematics and Computation, 215 (2010), 10, pp. 3631-3644
  20. Ma, W. X., et al., A Bilinear Backlund Transformation of a (3+1)-Dimensional Generalized KP Equation, Physics Letter A, 25 (2012), 10, pp. 1500-1504
  21. Wazwaz, A. M., Multiple-Soliton Solutions for a (3+1)-Dimensional Generalized KP Equation, Communications in Non-Linear Science and Numerical Simulation, 17 (2012), 2, pp. 491-495
  22. Ma, W. X., et al., Wronskian and Grammian Solutions to a (3 +1)-Dimensional Generalized KP Equation, Applied Mathematics and Computation, 217 (2011), 24, pp. 10016-10023
  23. Xu, Z. H., et al., Rogue Wave for the (2+1)-Dimensional Kadomtsev-Petviashvili Equation, Applied Mathematical Letter, 37 (2014), Nov., pp. 34-38
  24. Chen, H. L., et al., Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation, Abstract and Applied Analysis, 2014 (2014), ID 378167
  25. Hirota, R., Fundamental Properties of the Binary Operators in Soliton Theory and Their Generalization, in: Dynamical Problem in Soliton Systems (Ed. S. Takeno), Springer Series in Synergetiecs, pp. 30, Springer, Berlin, 1985
  26. Dai, Z. D., et al., Applications of HTA and EHTA to YTSF Equation, Applied Mathematics and Computation, 207 (2009), 2, pp. 360-364
  27. Dai, Z. D., et al., Periodic Kink-Wave and Kinky Periodic-Wave Solutions for the Jimbo-Miwa Equation, Physics Letter A, 372 (2008), 38, pp. 5984-5986
  28. Xu, Z. H. et al., New Periodic Solitary-Wave Solutions for the Benjiamin Ono Equation, Applied Mathematics and Computation, 215 (2010), 12, pp. 4439-4442
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Kink degeneracy and rogue potential flow for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

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