Skip to main content
SpringerLink
Log in

Different wave patterns for (2 + 1) dimensional Maccari’s equation

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, we are concerned with the (2 + 1) dimensional Maccari’s equation. With the aid of Truncated Painlevé Approach (TPA), the localized solutions have obtained in terms of arbitrary functions. By using the suitable arbitrary functions present in the solution, we have generated the multi-rogue waves, rogue wave doublet and lump solutions. Moreover, through selecting the values of control parameters, dynamical behaviors for the obtained multi-rogue wave, rogue wave doublet and lump solutions are graphically illustrated with the aid of Mathematica tool. The results obtained through this investigation will be beneficial for understanding the dynamics of nonlinear waves in higher dimensional Maccari systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Lou, S.Y., Lu, J.: Special solutions from the variable separation approach: the Davey-Stewartson equation. J. Phys. A Math. Gen. 29, 4209–4215 (1996)

    Article  MathSciNet  Google Scholar 

  2. Xiao, Y., Fan, E., Liu, P.: Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions. J. Math. Anal. Appl. 504, 1255 (2021)

    Article  MathSciNet  Google Scholar 

  3. Lü, X., Hua, Y.F., Chen, S.J., Tang, X.F.: Integrability characteristics of a novel (2+1)-dimensional nonlinear model: Painlevé analysis, soliton solutions, Bäcklund transformation, Lax pair and infinitely many conservation laws. Commun. Nonlinear Sci. Numer. Simul. 95, 105612 (2021)

    Article  Google Scholar 

  4. Hirota, R.: Exact envelope-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14, 805–809 (1973)

    Article  MathSciNet  Google Scholar 

  5. Guo, B., Ling, L., Liu, Q.P.: Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. Phys. Rev. E. 85, 026607 (2012)

    Article  Google Scholar 

  6. Yin, Z.Y., Tian, S.F.: Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada-Kotera equation. Phys. D: Nonlinear Phenomena. 427, 133002 (2021)

    Article  MathSciNet  Google Scholar 

  7. Radha, R., Tang, X.Y., Lou, S.Y.: Truncated Painlevé expansion – a unified approach to exact solutions and Dromion interactions of (2+1)-dimensional nonlinear systems. Z. Naturforsch. 62, 107–116 (2007)

    Article  Google Scholar 

  8. Tian, S.F.: Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized Boussinesq water wave equation. Appl. Math. Lett. 100, 106056 (2020)

    Article  MathSciNet  Google Scholar 

  9. Wang, Z.Y., Tian, S.F., Cheng, J.: The \(\overline{\partial }\)-dressing method and soliton solutions for the three-component coupled Hirota equations. J. Math. Phys. 62, 093510 (2021)

  10. Demiray, S.T., Pandir, Y., Bulut, H.: New solitary wave solutions of Maccari system. Ocean Eng. 103, 153–159 (2015)

    Article  Google Scholar 

  11. Maccari, A.: The Maccari system as model system for rogue waves. Phys. Lett. A. 384, 126740–126746 (2020)

    Article  MathSciNet  Google Scholar 

  12. Dysthe, K., Krogstad, H.E., Peter, M.: Oceanic rogue waves. Ann. Rev. Fluid Mech. 40, 287–310 (2008)

    Article  MathSciNet  Google Scholar 

  13. Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Optical rogue waves. Nature 450, 1054–1057 (2007)

    Article  Google Scholar 

  14. Tian, Y., Liu, J.G.: Study on dynamical behavior of multiple lump solutions and interaction between solitons and lump wave. Nonlinear Dyn 104, 1507–1517 (2021)

    Article  Google Scholar 

  15. Ma, Y.L., Wazwaz, A.M., Li, B.Q.: New extended Kadomtsev-Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions. Nonlinear Dyn. 104, 1581–1594 (2021)

    Article  Google Scholar 

  16. Subramanian, K., Alagesan, T., Mahalingam, A., Mani Rajan, M.S.: Propagation properties of optical soliton in an erbium-doped tapered parabolic index nonlinear fiber: soliton control. Nonlinear Dyn. 87, 1575–1587 (2017)

    Article  Google Scholar 

  17. Ohta, Y., Yang, J.K.: General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation. Proc. R. Soc. A. 468, 1716–1740 (2012)

    Article  MathSciNet  Google Scholar 

  18. Ohta, Y., Yang, J.K.: Rogue waves in the Davey-Stewartson I equation. Phys. Rev. E 86, 036604 (2012)

    Article  Google Scholar 

  19. Radha, R., Senthil Kumar, C., Subramanian, K.: Drone like dynamics of dromion pairs in the (2+1) AKNS equation. Comput. Math. Appl. 75, 2356–2364 (2018)

    Article  MathSciNet  Google Scholar 

  20. Subramanian, K., Senthil Kumar, C., Radha, R., Alagesan, T.: Elusive noninteracting localized solutions of (2+1)-dimensional Maccari equation. Rom. Rep. Phys. 69, 1–16 (2017)

    Google Scholar 

  21. Tian, S.F., Guo, D., Wang, X., Zhang, T.: Traveling wave, lump wave, rogue wave, multi-kink solitary wave and interaction solutions in a (3+1)-dimensional Kadomtsev - Petviashvili equation with Bäcklund transformation. J. Appl. Anal. Comput. 11, 45–58 (2021)

    MathSciNet  Google Scholar 

  22. Maccari, A.: Universal and integrable nonlinear evolution systems of equations in (2+1) dimensions. J. Math. Phys. 38, 4151–4166 (1997)

    Article  MathSciNet  Google Scholar 

  23. Han, Z., Chen, Y.: Bright-dark mixed N-soliton solution of the two-dimensional Maccari system. Chin. Phys. Lett. 34, 070202–070205 (2017)

    Article  Google Scholar 

  24. Cheemaa, N., Younis, M.: New and more exact travelling wave solutions to integrable (2+1)-dimensional Maccari system. Nonlinear Dyn. 83, 1395–1401 (2016)

    Article  Google Scholar 

  25. Tian, S.F., Tu, J.M., Zhang, T.T., Chen, Y.R.: Integrable discretizations and soliton solutions of an Eckhaus-Kundu equation. Appl. Math. Lett. 122, 1075 (2021)

    Article  MathSciNet  Google Scholar 

  26. Radha, R., Lakshmanan, M.: The (2+1) dimensional sine-Gordon equation; integrability and localized solution. J. Phys. A: Math. Gen. 29, 1551–1562 (1996)

    Article  MathSciNet  Google Scholar 

  27. Uthayakumar, A., Nakkeeran, K., Porsezian, K.: Soliton solution of new (2+1)-dimensional nonlinear partial differential equations. Chaos Solitons Fractals. 10, 1513–1518 (1999)

    Article  MathSciNet  Google Scholar 

  28. Lai, D.W.C., Chow, K.W.: Coalescence of ripplons, breathers, dromions and dark solitons. J. Phys. Soc. Jpn. 70, 666–677 (2001)

    Article  Google Scholar 

  29. Yuan, F., Rao, J., Porsezian, K., Mihalache, D., He, J.: Various exact rational solutions of the two-dimensional Maccari’s system. Rom. J. Phys. 61, 378–399 (2016)

    Google Scholar 

  30. Radha, R., Senthil Kumar, C., Lakshmanan, M., Tang, X.Y., Lou, S.Y.: Periodic and localized solutions of the long wave–short wave resonance interaction equation. J Phys. A. 38, 9649–9663 (2005)

    Article  MathSciNet  Google Scholar 

  31. Radha, R., Senthil Kumar, C., Lakshmanan, M., Gilson, C.R.: The collision of multimode dromions and a firewall in the two-component long-wave–short-wave resonance interaction equation. J. Phys. A: Math. Theor. 42, 102002 (2009)

    Article  MathSciNet  Google Scholar 

  32. Peng, Y.: A class of doubly periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation. Phys. Lett. A. 337, 55–60 (2005)

    Article  MathSciNet  Google Scholar 

  33. Radha, R., Lakshmanan, M.: Singularity analysis and localized coherent structures in (2 + 1)- dimensional generalized Korteweg de Vries equations. J. Math. Phys. 35, 4746–4756 (1994)

    Article  MathSciNet  Google Scholar 

  34. Yang, J., Zhang, Y.L., Ma, L.Y.: Multi-rogue wave solutions for a generalize integrable discrete nonlinear Schrödinger equation with higher order excitations. Nonlinear Dyn. 105, 629–641 (2021)

    Article  Google Scholar 

  35. Liu, W.H., Zhang, Y.F.: Multiple-rogue wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation. Z. Angew. Math. Phys. 70, 112 (2019)

    Article  MathSciNet  Google Scholar 

  36. Yanlin, Y., Liu, J., Bu, L., Pan, C., Chen, S., Mihalache, D.: Rogue waves and modulation instability in an extended Manakov system. Nonlinear Dyn. 102, 06029 (2020)

    Google Scholar 

  37. Wu, J.W., Deng, Y.J., Lin, J.: Interactions solutions of various-type rogue with multi-stripe solitons and breather lump for the (2 + 1) dimensional Maccari’s system. Int. J. Mod. Phys. B 34, 2050268–2050281 (2020)

    Article  MathSciNet  Google Scholar 

  38. Radha, B., Duraisamy, C.: The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations. J. Ambient Intell. Hum. Comput. 12, 6591–6659 (2021)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Science and Humanities, Jerusalem College of Engineering, Chennai, India

    J. Thilakavathy

  2. Department of Physics, KCG College of Technology, Chennai, India

    R. Amrutha

  3. Department of Physics, SRM Institute of Science and Technology, Ramapuram Campus, Chennai, India

    K. Subramanian

  4. Department of Physics, University College of Engineering, Anna University, Ramanathapuram, India

    M. S. Mani Rajan

Authors
  1. J. Thilakavathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Amrutha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Subramanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. S. Mani Rajan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. S. Mani Rajan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of this manuscript.

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thilakavathy, J., Amrutha, R., Subramanian, K. et al. Different wave patterns for (2 + 1) dimensional Maccari’s equation. Nonlinear Dyn 108, 445–456 (2022). https://doi.org/10.1007/s11071-021-07179-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-07179-4

Keywords

Search

Navigation