Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

Volume 10, Issue 2, pp 521--527 http://dx.doi.org/10.22436/jnsa.010.02.17

Publication Date: February 20, 2017 Submission Date: September 07, 2016

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Authors

Zhenhui Xu - School of Science, Southwest University of Science and Technology, Mianyang 621010, P. R. China. Hanlin Chen - School of Science, Southwest University of Science and Technology, Mianyang 621010, P. R. China. Zhengde Dai - School of Mathematics and Physics, Yunnan University, Kunming 650091, P. R. China.

Abstract

In this paper, the (3+1)-dimensional Kadomtsev-Petviashvili equation is investigated. Two kinds of periodic breather solitary wave and rogue wave solutions are obtained by using the two-wave method and the homoclinic breather limit approach with the aid of Maple. Deflection of rogue wave varying with the seed solution \(u_0\) is investigated.

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Keywords

• (3+1)-dimensional Kadomtsev-Petviashvili equation
• homoclinic breather limit approach
• two-wave method
• rational breather solutions
• rogue wave.

MSC

•  35G20
•  35C05
•  35C07

References

• [1] N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, Rogue waves and rational solutions of the nonlinear Schrödinger equation, Phys. Rev. E, 80 (2009), 2137–2145.
  • View Article
  • Google Scholar


• [2] N. Akhmediev, A. Ankiewicz, M. Taki, Waves that appear from nowhere and disappear without a trace, Phys. Lett. A, 373 (2009), 675–678.
  • View Article
  • Google Scholar
  • MATH


• [3] C.-L. Bai, C.-J. Bai, H. Zhao, A generalized variable-coefficient algebraic method exactly solving (3 + 1)-dimensional Kadomtsev-Petviashvilli equation, Commun. Theor. Phys. (Beijing), 44 (2005), 821–826.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] Y. V. Bludov, V. V. Konotop, N. Akhmediev, Matter rogue waves, Phys. Rev. A, 80 (2009), 033610.
  • View Article
  • Google Scholar


• [5] H.-L. Chen, Z.-H. Xu, Z.-D. Dai, Rogue wave for the (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation, Abstr. Appl. Anal., 2014 (2014 ), 7 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] Z.-D. Dai, J. Liu, D.-L. Li, Applications of HTA and EHTA to YTSF equation, Appl. Math. Comput., 207 (2009), 360–364.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] C.-Q. Dai, G.-Q. Zhou, J.-F. Zhang, Controllable optical rogue waves in the femtosecond regime, Phys. Rev. E, 85 (2012), 016603.
  • View Article
  • Google Scholar


• [8] K. Dysthe, H. E. Krogstad, P. Müller, Oceanic rogue waves, Annu. Rev. Fluid Mech., 40 (2008), 287–310,40, Annual Reviews, Palo Alto, CA (2008)
  • View Article
  • MathSciNet
  • Google Scholar


• [9] C. Kharif, E. Pelinovsky, A. Slunyaey, Rogue waves in the ocean, Advances in Geophysical and Environmental Mechanics and Mathematics, Springer-Verlag, Berlin (2009)
  • MathSciNet
  • Google Scholar


• [10] Z.-Y. Ma, S.-H. Ma, Analytical solutions and rogue waves in (3+ 1)-dimensional nonlinear Schrödinger equation, Chin. Phys. B, 21 (2012), 030507.
  • Google Scholar


• [11] D. R. Solli, C. Ropers, B. Jalali , Active control of rogue waves for stimulated supercontinuum generation, Phys. Rev. Lett., 101 (2008), 233902.
  • View Article
  • Google Scholar


• [12] L. Stenflo, M. Marklund, Rogue waves in the atmosphere, J. Plasma Phys., 76 (2010), 293–306.
  • View Article
  • Google Scholar


• [13] L.-Y. Wang, S.-Y. Lou, Some special types of solitary wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvilli equation, Commun. Theor. Phys. (Beijing), 33 (2000), 683–686.
  • View Article
  • MathSciNet
  • Google Scholar


• [14] R.-Q. Wu, Bilinear Bäklund transformation and explicit solutions for nonlinear evolution equation, Chin. Phys. B, 19 (2010), 040304.


• [15] Z.-H. Xu, H.-L. Chen, Z.-D. Dai , Rogue wave for the (2 + 1)-dimensional Kadomtsev-Petviashvili equation, Appl. Math. Lett., 37 (2014), 34–38.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] Z.-H. Xu, H.-L. Chen, M.-R. Jiang, Z.-D. Dai, W. Chen, Resonance and deflection of multi-soliton to the (2 + 1)- dimensional Kadomtsev-Petviashvili equation, Nonlinear Dynam., 78 (2014), 461–466.
  • View Article
  • MathSciNet
  • Google Scholar


• [17] Z.-H. Xu, D.-Q. Xian, H.-L. Chen, New periodic solitary-wave solutions for the Benjiamin Ono equation, Appl. Math. Comput., 215 (2010), 4439–4442.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] Z.-Y. Yan, Nonautonomous rogons in the inhomogeneous nonlinear Schrödinger equation with variable coefficients, Phys. Lett. A, 374 (2010), 672–681.
  • View Article
  • Google Scholar
  • MATH


• [19] X.-J. Yang, A new integral transform method for solving steady heat-transfer problem, Therm. Sci., 20 (2016), 639–642.
  • Google Scholar


• [20] X.-J. Yang, A new integral transform with an application in heat-transfer problem, Therm. Sci., 20 (2016), 677–681.
  • View Article
  • Google Scholar