Generation of Solitary Waves with Analytical Solution for The (3+1)-dimensional pKP-BKP Equation and Reductions

Year 2024, Volume: 13 Issue: 3, 822 - 835, 26.09.2024

Fatma Nur Kaya Sağlam

https://doi.org/10.17798/bitlisfen.1494900

Cited By: 2

Abstract

In this study, new solitary wave solutions are obtained for the combination of the B-type Kadomtsev-Petviashvili (BKP) equation and the potential Kadomtsev-Petviashvili (pKP) equation, called the integrable (3+1)-dimensional coupled pKP-BKP equation, and its two reduced forms. For this purpose, the Bernoulli auxiliary equation method, which is an ansatz-based method, is used. As a result, kink, lump, bright soliton and breather wave solutions are observed. It is concluded that this method and the results obtained for the considered pKP -BKP equations are an important step for further studies in this field.

Keywords

Solitary waves , Kadomtsev-Petviashvili equation , Bernoulli auxilary equation method , B-type Kadomtsev-Petviashvili equation.

References

• [1] I. R. Rahmonov, J. Tekić, P. Mali, A. Irie, A. Plecenik, and Y. M. Shukrinov, “Resonance phenomena in an annular array of underdamped Josephson junctions,” Physical Review B, vol. 101, no. 17, p. 174515, 2020.
• [2] L. F. Guo and W. R. Xu, “The traveling wave mode for nonlinear Biswas–Milovic equation in magneto-optical wave guide coupling system with Kudryashov’s law of refractive index,” Results in Physics, vol. 27, p. 104500, 2021.
• [3] J. J. Su, Y. T. Gao, and C. C. Ding, “Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows,” Applied Mathematics Letters, vol. 88, pp. 201–208, 2019.
• [4] S. Kumar and S. K. Dhiman, “Lie symmetry analysis, optimal system, exact solutions and dynamics of solitons of a (3+ 1)-dimensional generalised BKP–Boussinesq equation,” Pramana, vol. 96, no. 1, p. 31, 2022.
• [5] Y. Liu and Y. Yang, “Rogue wave solutions for the 3+ 1-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili equation,” Chinese Journal of Physics, vol. 86, pp. 508-514, 2023.
• [6] K. Dysthe, H. E. Krogstad, and P. Müller, “Oceanic rogue waves,” Annu. Rev. Fluid Mech., vol. 40, pp. 287-310, 2008.
• [7] J. M. Dudley, G. Genty, A. Mussot, A. Chabchoub, and F. Dias, “Rogue waves and analogies in optics and oceanography,” Nature Reviews Physics, vol. 1, no. 11, pp. 675-689, 2019.
• [8] H. Chen and J. L. Bona, “Periodic traveling-wave solutions of nonlinear dispersive evolution equations”, 2013.
• [9] Y. Zhang, J. W. Yang, K. W. Chow, and C. F. Wu, "Solitons, breathers and rogue waves for the coupled Fokas–Lenells system via Darboux transformation," Nonlinear Analysis: Real World Applications, vol. 33, pp. 237-252, 2017.
• [10] B. Frisquet, B. Kibler, and G. Millot, “Collision of Akhmediev breathers in nonlinear fiber optics,” Physical Review X, vol. 3, no. 4, p. 041032, 2013.
• [11] K.-J. Wang, "Soliton molecules and other diverse wave solutions of the (2+1)-dimensional Boussinesq equation for the shallow water," Eur. Phys. J. Plus, vol. 138, article number 891, 2023.
• [12] J. Ahmad and Z. Mustafa, "Analysis of soliton solutions with different wave configurations to the fractional coupled nonlinear Schrödinger equations and applications," Opt. Quantum Electron., vol. 55, article number 1228, 2023.
• [13] A. Ali, J. Ahmad, and S. Javed, "Investigating the dynamics of soliton solutions to the fractional coupled nonlinear Schrödinger model with their bifurcation and stability analysis," Opt. Quantum Electron., vol. 55, article number 829, 2023.
• [14] M. Wadati, K. Konno, and Y. H. Ichikawa, "New integrable nonlinear evolution equations," Journal of the Physical Society of Japan, vol. 47, no. 5, pp. 1698-1700, 1979.
• [15] A. M. Wazwaz, "Two kinds of multiple wave solutions for the potential YTSF equation and a potential YTSF-type equation," J Appl Nonlinear Dyn, vol. 1, pp. 51–8, 2012.
• [16] R. Hirota, "The direct method in soliton theory," Cambridge University Press, 2004.
• [17] A. M. Wazwaz, "Partial differential equations and solitary waves theory," Springer and HEP, Berlin, 2009.
• [18] A. M. Wazwaz, "Two kinds of multiple wave solutions for the potential YTSF equation and a potential YTSF-type equation," J Appl Nonlinear Dyn, vol. 1, pp. 51–8, 2012.
• [19] S. Y. Zhu, D.-X. Kpng, and Lou, "Dark KortewegDe Vrise System and its higher-dimensional deformations," Chin Phys Lett, vol. 40, p. 080201, 2023.
• [20] A. M. Wazwaz, "New painlevé integrable (3+1)-dimensional combined pKP-BKP equation: Lump and multiple soliton solutions," Chinese Phys Lett, vol. 40, p. 12050, 2023.
• [21] W. X. Ma, "N-soliton solution of a combined pKP–BKP equation," J Geom Phys, vol. 165, p. 104191, 2021.
• [22] Y. Feng and S. Bilige, "Resonant multi-soliton, M-breather, M-lump and hybrid solutions of a combined pKP–BKP equation," J Geom Phys, vol. 169, p. 104322, 2021.
• [23] Z.-Y. Ma, J.-X. Fei, W.-P. Cao, and H.-L. Wu, "The explicit solution and its soliton molecules in the (2+1)-dimensional pKP-BKP equation," Results Phys, vol. 35, p. 105363, 2022.
• [24] K. U. Tariq, A. M. Wazwaz, and R. N. Tufail, "Lump, periodic and travelling wave solutions to the (2+1)-dimensional pKP–BKP model," Eur Phys J Plus, vol. 137, p. 1100, 2022.
• [25] F. N. K. Sağlam and S. Ahmad, "Stability analysis and retrieval of new solitary waves of (2+ 1)-and (3+ 1)-dimensional potential Kadomtsev–Petviashvili and B-type Kadomtsev–Petviashvili equations using auxiliary equation technique," Modern Physics Letters B, vol. 2450413, 2024.
• [26] A. M. Wazwaz, "Breather wave solutions for an integrable (3+ 1)-dimensional combined pKP–BKP equation," Chaos, Solitons & Fractals, vol. 182, p. 114886, 2024.
• [27] A. M. Wazwaz, "Abundant solutions of distinct physical structures for three shallow water waves models," Discontinuity Nonlinearity Complex, vol. 6, pp. 295–304, 2017.
• [28] A. M. Wazwaz, "A variety of distinct kinds of multiple soliton solutions for a (3+1)-dimensional nonlinear evolution equations," Math Methods Appl Sci, vol. 36, pp. 349–57, 2013.
• [29] A. R. Adem and C. M. Khalique, "New exact solutions and conservation laws of a coupled Kadomtsev–Petviashvili system," Comput & Fluids, vol. 81, pp. 10–6, 2013.
• [30] Z. Pinar, "Analytical studies for the Boiti–Leon–Monna–Pempinelli equations with variable and constant coefficients," Asymptotic Analysis, vol. 117, no. 3-4, pp. 279-287, 2020.
• [31] V. Ala, "Exact solutions of nonlinear time fractional Schrödinger equation with beta-derivative," Fundamentals of Contemporary Mathematical Sciences, vol. 4, no. 1, pp. 1-8, 2023.
• [32] F. S. V. Causanilles, H. M. Baskonus, J. L. G. Guirao, and G. R. Bermúdez, "Some important points of the Josephson effect via two superconductors in complex bases," Mathematics, vol. 10, no. 15, article 2591, 2022.
• [33] H. M. Baskonus, A. A. Mahmud, K. A. Muhamad, and T. Tanriverdi, "A study on Caudrey–Dodd–Gibbon–Sawada–Kotera partial differential equation," Mathematical Methods in the Applied Sciences, vol. 45, no. 14, pp. 8737-8753, 2022.
• [34] A. Hussain, H. Ali, F. Zaman, and N. Abbas, "New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method," International Journal of Mathematics and Computer in Engineering, vol. 2, no. 1, pp. 35-58, 2023.