Dark soliton solutions to (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation via the first integral method

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


     In the present work, the First Integral Method is being applied in finding a non-soliton as well as a soliton solution of the ( 2 + 1 ) dimensional Kundu-Mukherjee-Naskar (KMN) equation which is a variant of the well-known Nonlinear Schrodinger ( NLS ) equation. Using the method, a dark optical soliton solution and a periodic trigonometric solution to the KMN equation have been suggested and the relevant conditions which guarantee the existence of such solutions are also indicated therein.

     

     


  • Keywords


    Kundu-Mukherjee-Naskar Equation; First Integral Method.

  • References


      [1] Aliyu, A. I., Li, Y. and Baleanu, D. “Single and Combined Optical Solitons and Conservation Laws in (2+1)-Dimensions with Kundu- Mukherjee- Naskar Equation”, Chin. J. Phys., (2019). https://doi.org/10.1016/j.cjph.2019.11.001.

      [2] Sulaiman, T. A. and Bulut, H. “The new extended rational SGEEM for construction of optical solitons to the (2+1)– dimensional Kundu–Mukhejee – Naskar model”, Applied Mathematics and Nonlinear Sciences, 4(2), 513–522(2019). https://doi.org/10.2478/AMNS.2019.2.00048.

      [3] Ekici, M., Sonmezoglu, A., Biswas, A. and Belic M. R. “Optical solitons in (2+1)–Dimensions with Kundu–Mukherjee–Naskar equa-tion by extended trial function scheme”, Chin. J. Phys. 57, 72 – 77 (2019). https://doi.org/10.1016/j.cjph.2018.12.011.

      [4] Yildrim, Y. “Optical solitons to Kundu–Mukherjee–Naskar model with trial equation approach”, Optik, 183, 1061 – 1065(2019). https://doi.org/10.1016/j.ijleo.2019.02.117.

      [5] Singh, S., Mukherjee,A., Sakkaravarthi, K. and Murugesan,K.. “Higher dimensional localized and periodic wave dynamics in a new integrable (2+1)- dimensional Kundu-Mukherjee-Naskar-model”, arXiv: 2001.06766v 1 [nlin. PS] 19 Jan 2020.

      [6] Talarposhti, R. A., Jalili, P., Rezazadeh, H., Jalili, B., Ganji, D. D., Adel, W. and Bekir, A. “ Optical soliton solutions to the (2 + 1)-dimensional Kundu-Mukherjee-Naskar equation”, Int. J. Mod. Phys. B, 2050102 (2020). https://doi.org/10.1142/S0217979220501027.

      [7] F., Haas, Mahmood, S. “Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons, arXiv:1712.05339v 1 [physics. Plasm-ph] 14 Dec 2017. https://doi.org/10.1103/PhysRevE.94.033212.

      [8] Guo, M., Fu, C., Zhang, Y, Liu, J. and Yang, H. “ Study of Ion-Acoustic Solitary Waves in a Magnetized Plasma Using the Three-Dimensional Time- Space Fractional Schamel-KdV Equation”, Complexity, Volume 2018, Article ID 6852548, 17 pages https://doi.org/10.1155/2018/6852548.

      [9] Feng, Z.S. “The first integral method to study the Burgers Korteweg-de Vries equation”, J. Phys. A, 35 (2), 343 – 349, (2002). https://doi.org/10.1088/0305-4470/35/2/312.

      [10] Feng, Z. S. “On explicit exact solu-tions to the compound Burg ers- Korteweg-de Vries equation”, Phys. Lett. A., Vol.293, 57 – 66 (2002). https://doi.org/10.1016/S0375-9601(01)00825-8.

      [11] Feng, Z. S. “Travelling wave behavior for a generalized Fisher equation”, Chaos, Soliton. Fract., Vol. 38, 481 – 488(2008). https://doi.org/10.1016/j.chaos.2006.11.031.

      [12] Feng, Z. S. “Exact solution to an approximate sine- Gordon equa-tion in (n + 1) – dimensional space”, Phys. Lett. A, Vol.302, 64 – 76 (2002). https://doi.org/10.1016/S0375-9601(02)01114-3.

      [13] Feng, Z. S. and Wang, X. H. “The first integral method to the two-dimensional Burgers- KdV equation”, Phys. Lett. A., Vol. 308, 173 – 178 (2002). https://doi.org/10.1016/S0375-9601(03)00016-1.

      [14] Feng, Z. S. and Knobel, R. “Travelling waves to a Burgers- Korteweg – de Vries equation with higher order nonlinearities”, J. Math. Anal. Appl., Vol.328, No. 2, 1435 – 1450 (2007). https://doi.org/10.1016/j.jmaa.2006.05.085.

      [15] Zhang, Z., Zhong, J., Dou, S. S., Liu, J., Peng, D. and Gao, T. “First Integral Method and Exact Solutions to Nonlinear Partial Differen-tial Equa tions arising in Mathematical Physics”, Rom. Rep. Phys. 65(4), 1155-1169 (2013).

      [16] Singh, S. S. “Soliton solutions of a generalized Klein–Gordon equation with power-law nonlinearity via the first integral method”, International Journal of Mathematics and Physics 9, №2,116-121 (2018). https://doi.org/10.26577/ijmph.2018.v9i2.268.


 

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Article ID: 30990
 
DOI: 10.14419/ijpr.v8i2.30990




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