Solitary wave analysis of the Kadomtsev–Petviashvili model in mathematical physics

References

• Ablowitz, M. J., & Segur, H. (1979). On the evolution of packets of water waves. Journal of Fluid Mechanics, 92(4), 691–715. doi:10.1017/S0022112079000835
   Google Scholar
• Ablowitz, M. J., & Segur, H. (1981). Solitons and the inverse scattering transform. Philadelphia: Society for Industrial and Applied Mathematics.
   Google Scholar
• Ali, I., Seadawy, A. R., Rizvi, S. T. R., Younis, M., & Ali, K. (2020). Conserved quantities along with Painleve analysis and Optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model. International Journal of Modern Physics B, 34(30), 2050283. doi:10.1142/S0217979220502835
   Web of Science ®Google Scholar
• Arqub, O. A., Tayebi, S., Baleanu, D., Osman, M. S., Mahmoud, W., & Alsulami, H. (2022). A numerical combined algorithm in cubic B-spline method and finite difference technique for the time-fractional nonlinear diffusion wave equation with reaction and damping terms. Results in Physics, 41, 105912. doi:10.1016/j.rinp.2022.105912
   Web of Science ®Google Scholar
• Baskonus, H. M., & Bulut, H. (2015). An effective schema for solving some nonlinear partial differential equations arising in nonlinear physics. Open Physics, 13(1). doi:10.1515/phys-2015-0035
   Web of Science ®Google Scholar
• Baskonus, H. M., & Gómez-Aguilar, J. F. (2019). New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with M-derivative. Modern Physics Letters B, 33(21), 1950251. doi:10.1142/S0217984919502518
   Web of Science ®Google Scholar
• Baskonus, H. M., & Kayan, M. (2023). Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations. Applied Mathematics & Nonlinear Sciences, 8(1), 81-100.
   Google Scholar
• Baskonus, H. M., Sulaiman, T. A., & Bulut, H. (2017). New solitary wave solutions to the (2 + 1)-dimensional Calogero–Bogoyavlenskii–Schiff and the Kadomtsev–Petviashvili hierarchy equations. Indian Journal of Physics, 91(10), 1237–1243. doi:10.1007/s12648-017-1033-z
   Web of Science ®Google Scholar
• Biondini, G., & Pelinovsky, D. (2008). Kadomtsev–Petviashvili equation. Scholarpedia, 3(10), 6539. doi:10.4249/scholarpedia.6539
   Google Scholar
• Bo, W. B., Wang, R. R., Fang, Y., Wang, Y. Y., & Dai, C. Q. (2023). Prediction and dynamical evolution of multipole soliton families in fractional Schrödinger equation with the PT-symmetric potential and saturable nonlinearity. Nonlinear Dynamics, 111(2), 1577–1588. doi:10.1007/s11071-022-07884-8
   Web of Science ®Google Scholar
• Chakravarty, S., & Kodama, Y. (2009). Soliton solutions of the KP equation and application to shallow water waves. Studies in Applied Mathematics, 123(1), 83–151. doi:10.1111/j.1467-9590.2009.00448.x
   Web of Science ®Google Scholar
• Cheemaa, N., Seadawy, A. R., & Chen, S. (2019). Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics. The European Physical Journal Plus, 134(3), 117. doi:10.1140/epjp/i2019-12467-7
   Web of Science ®Google Scholar
• Chen, S., & Ren, Y. (2022). Small amplitude periodic solution of Hopf bifurcation theorem for fractional differential equations of balance point in group competitive martial arts. Applied Mathematics & Nonlinear Sciences, 7(1), 207–214. doi:10.2478/amns.2021.2.00152
   Google Scholar
• Deng, Y. S., Tian, B., Sun, Y., Zhang, C. R., & Hu, C. C. (2019). Rational and semi-rational solutions for the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Modern Physics Letters B, 33(25), 1950296. doi:10.1142/S0217984919502968
   Web of Science ®Google Scholar
• Dhiman, S. K., & Kumar, S. (2022). Different dynamics of invariant solutions to a generalized (3 + 1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation arising in shallow water-waves. Journal of Ocean Engineering & Science. https://doi.org/10.1016/j.joes.2022.06.019
   Google Scholar
• Djennadi, S., Shawagfeh, N., Inc, M., Osman, M. S., Gómez-Aguilar, J. F., & Abu Arqub, O. (2021). The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique. Physica Scripta, 96(9), 094006. doi:10.1088/1402-4896/ac0867
   Web of Science ®Google Scholar
• Fang, J. J., Mou, D. S., Zhang, H. C., & Wang, Y. Y. (2021). Discrete fractional soliton dynamics of the fractional Ablowitz–Ladik model. Optik, 228, 166186. doi:10.1016/j.ijleo.2020.166186
   Web of Science ®Google Scholar
• Fang, Y., Wu, G. Z., Wang, Y. Y., & Dai, C. Q. (2021). Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN. Nonlinear Dynamics, 105(1), 603–616. doi:10.1007/s11071-021-06550-9
   Web of Science ®Google Scholar
• Fatema, K., Islam, M. E., Arafat, S. Y., & Akbar, M. A. (2022). Solitons’ behavior of waves by the effect of linearity and velocity of the results of a model in magnetized plasma field. Journal of Ocean Engineering & Science. doi:10.1016/j.joes.2022.07.003
   Google Scholar
• García Guirao, J. L., Baskonus, H. M., Kumar, A., Rawat, M. S., & Yel, G. (2019). Complex patterns to the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation. Symmetry, 12(1), 17. doi:10.3390/sym12010017
   Google Scholar
• Geng, K. L., Mou, D. S., & Dai, C. Q. (2023). Nondegenerate solitons of 2-coupled mixed derivative nonlinear Schrödinger equations. Nonlinear Dynamics, 111(1), 603–617. doi:10.1007/s11071-022-07833-5
   Web of Science ®Google Scholar
• Groves, M. D., & Sun, S. M. (2008). Fully localised solitary-wave solutions of the three-dimensional gravity–capillary water-wave problem. Archive for Rational Mechanics & Analysis, 188(1), 1–91. doi:10.1007/s00205-007-0085-1
   Web of Science ®Google Scholar
• Hammack, J., Mccallister, D., Scheffner, N., & Segur, H. (1995). Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves. Journal of Fluid Mechanics, 285, 95–122. doi:10.1017/S0022112095000474
   Web of Science ®Google Scholar
• Hammack, J., Scheffner, N., & Segur, H. (1989). Two-dimensional periodic waves in shallow water. Journal of Fluid Mechanics, 209, 567–589. doi:10.1017/S0022112089003228
   Web of Science ®Google Scholar
• Haupt, S. E. (1988). Solving nonlinear wave problems with spectral boundary value techniques. Michigan: University of Michigan.
   Google Scholar
• Islam, M. E., & Akbar, M. A. (2020). Stable wave solutions to the Landau–Ginzburg–Higgs equation and the modified equal width wave equation using the IBSEF method. Arab Journal of Basic & Applied Sciences, 27(1), 270–278. doi:10.1080/25765299.2020.1791466
   Google Scholar
• Islam, M. E., Kundu, P. R., Akbar, M. A., Gepreel, K. A., & Alotaibi, H. (2021). Study of the parametric effect of self-control waves of the Nizhnik-Novikov–Veselov equation by the analytical solutions. Results in Physics, 22, 103887. doi:10.1016/j.rinp.2021.103887
   Web of Science ®Google Scholar
• Ismael, H. F., Akkilic, A. N., Murad, M. A. S., Bulut, H., Mahmoud, W., & Osman, M. S. (2022). Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions. Nonlinear Dynamics, 110(4), 3699–3712. doi:10.1007/s11071-022-07817-5
   Web of Science ®Google Scholar
• Ismael, H. F., Bulut, H., Baskonus, H. M., & Gao, W (2021). Dynamical behaviors to the coupled Schrödinger–Boussinesq system with the beta derivative. AIMS Mathematics, 6(7), 7909–7928. doi:10.3934/math.2021459
   Web of Science ®Google Scholar
• Ismael, H. F., Bulut, H., Park, C., & Osman, M. S. (2020). M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Results in Physics, 19, 103329. doi:10.1016/j.rinp.2020.103329
   Web of Science ®Google Scholar
• Ismael, H. F., Sulaiman, T. A., Nabi, H. R., Mahmoud, W., & Osman, M. S. (2023). Geometrical patterns of time variable Kadomtsev–Petviashvili (I) equation that models dynamics of waves in thin films with high surface tension. Nonlinear Dynamics, 111(10), 9457–9466. doi:10.1007/s11071-023-08319-8
   Web of Science ®Google Scholar
• Jawad, A. J. A. M., & Adham, A. A. (2013). Soliton solution to the (3 + 1)-dimensional Kadomtsev–Petviashvili equation by the tanh–coth method. International Journal of Scientific & Engineering Research, 4(9), 2005–2010.
   Google Scholar
• Kadomtsev, B. B., & Petviashvili, V. I. (1970). On the stability of solitary waves in weakly dispersing media. In Doklady Akademii Nauk, 192(4), 753–756. (Russian Academy of Sciences).
   Web of Science ®Google Scholar
• Kumar, A., Ilhan, E., Ciancio, A., Yel, G., & Baskonus, H. M (2021). Extractions of some new travelling wave solutions to the conformable Date–Jimbo–Kashiwara–Miwa equation. AIMS Mathematics, 6(5), 4238–4264. doi:10.3934/math.2021251
   Web of Science ®Google Scholar
• Kumar, S., & Dhiman, S. K. (2022). Lie symmetry analysis, optimal system, exact solutions and dynamics of solitons of a (3 + 1)-dimensional generalised BKP–Boussinesq equation. Pramana, 96(1), 31. doi:10.1007/s12043-021-02269-9
   Web of Science ®Google Scholar
• Kumar, S., & Mann, N. (2022). Abundant closed-form solutions of the (3 + 1)-dimensional Vakhnenko–Parkes equation describing the dynamics of various solitary waves in ocean engineering. Journal of Ocean Engineering & Science. doi:10.1016/j.joes.2022.04.007
   Google Scholar
• Kumar, S., & Rani, S. (2020). Lie symmetry reductions and dynamics of soliton solutions of (2 + 1)-dimensional Pavlov equation. Pramana, 94(1), 116. doi:10.1007/s12043-020-01987-w
   Web of Science ®Google Scholar
• Kumar, S., & Rani, S. (2021). Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2 + 1)-dimensional dissipative long wave system. Physica Scripta, 96(12), 125202. doi:10.1088/1402-4896/ac1990
   Web of Science ®Google Scholar
• Kumar, S., Rani, S., & Mann, N. (2022). Diverse analytical wave solutions and dynamical behaviors of the new (2 + 1)-dimensional Sakovich equation emerging in fluid dynamics. The European Physical Journal Plus, 137(11), 1226. doi:10.1140/epjp/s13360-022-03397-w
   Web of Science ®Google Scholar
• Li, B. Q., & Ma, Y. L. (2017). Periodic solutions and solitons to two complex short pulse (CSP) equations in optical fiber. Optik, 144, 149–155. doi:10.1016/j.ijleo.2017.06.114
   Web of Science ®Google Scholar
• Malik, S., Almusawa, H., Kumar, S., Wazwaz, A. M., & Osman, M. S. (2021). A (2 + 1)-dimensional Kadomtsev–Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions. Results in Physics, 23, 104043. doi:10.1016/j.rinp.2021.104043
   Web of Science ®Google Scholar
• Nisar, K. S., Ilhan, O. A., Abdulazeez, S. T., Manafian, J., Mohammed, S. A., & Osman, M. S. (2021). Novel multiple soliton solutions for some nonlinear PDEs via multiple Exp-function method. Results in Physics, 21, 103769. doi:10.1016/j.rinp.2020.103769
   Web of Science ®Google Scholar
• Nonlaopon, K., Mann, N., Kumar, S., Rezaei, S., & Abdou, M. A. (2022). A variety of closed-form solutions, Painlevé analysis, and solitary wave profiles for modified KdV–Zakharov–Kuznetsov equation in (3 + 1)-dimensions. Results in Physics, 36, 105394. doi:10.1016/j.rinp.2022.105394
   Web of Science ®Google Scholar
• Park, C., Nuruddeen, R. I., Ali, K. K., Muhammad, L., Osman, M. S., & Baleanu, D. (2020). Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations. Advances in Difference Equations, 2020(1), 1–12. doi:10.1186/s13662-020-03087-w
   PubMed Web of Science ®Google Scholar
• Pelinovsky, D. E., Stepanyants, Y. A., & Kivshar, Y. S. (1995). Self-focusing of plane dark solitons in nonlinear defocusing media. Physical Review. E, Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, 51(5), 5016–5026. doi:10.1103/physreve.51.5016
   PubMed Web of Science ®Google Scholar
• Peng, Y. Z., & Krishnan, E. V. (2005). Exact travelling wave solutions to the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Acta Physica Polonica A, 108(3), 421–428. doi:10.12693/APhysPolA.108.421
   Web of Science ®Google Scholar
• Rasool, T., Hussain, R., Al Sharif, M. A., Mahmoud, W., & Osman, M. S. (2023). A variety of optical soliton solutions for the M-truncated Paraxial wave equation using Sardar-subequation technique. Optical & Quantum Electronics, 55(5), 396. doi:10.1007/s11082-023-04655-6
   Web of Science ®Google Scholar
• Rizvi, S. T. R., Seadawy, A. R., Ashraf, F., Younis, M., Iqbal, H., & Baleanu, D. (2020). Lump and interaction solutions of a geophysical Korteweg–de Vries equation. Results in Physics, 19, 103661. doi:10.1016/j.rinp.2020.103661
   Web of Science ®Google Scholar
• Seadawy, A. (2016). Stability analysis of traveling wave solutions for generalized coupled nonlinear KdV equations. Applied Mathematics & Information Sciences, 10(1), 209–214. doi:10.18576/amis/100120
   Google Scholar
• Seadawy, A. R. (2014). Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Computers & Mathematics with Applications, 67(1), 172–180. doi:10.1016/j.camwa.2013.11.001
   Web of Science ®Google Scholar
• Seadawy, A. R., & Cheemaa, N. (2020). Some new families of spiky solitary waves of one-dimensional higher-order K–dV equation with power law nonlinearity in plasma physics. Indian Journal of Physics, 94(1), 117–126. doi:10.1007/s12648-019-01442-6
   Web of Science ®Google Scholar
• Seadawy, A. R., Kumar, D., Hosseini, K., & Samadani, F. (2018). The system of equations for the ion sound and Langmuir waves and its new exact solutions. Results in Physics, 9, 1631–1634. doi:10.1016/j.rinp.2018.04.064
   Web of Science ®Google Scholar
• Segur, H., & Finkel, A. (1985). An analytical model of periodic waves in shallow water. Studies in Applied Mathematics, 73(3), 183–220. doi:10.1002/sapm1985733183
   Web of Science ®Google Scholar
• Siddique, I., Jaradat, M. M., Zafar, A., Mehdi, K. B., & Osman, M. S. (2021). Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches. Results in Physics, 28, 104557. doi:10.1016/j.rinp.2021.104557
   Web of Science ®Google Scholar
• Triki, H., Biswas, A., Moshokoa, S. P., & Belic, M. (2017). Optical solitons and conservation laws with quadratic–cubic nonlinearity. Optik, 128, 63–70. doi:10.1016/j.ijleo.2016.10.010
   Web of Science ®Google Scholar
• Wang, J., Shehzad, K., Seadawy, A. R., Arshad, M., & Asmat, F. (2023). Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled Zakharov–Kuznetsov systems with their stability. Journal of Taibah University for Science, 17(1), 2163872. doi:10.1080/16583655.2022.2163872
   Web of Science ®Google Scholar
• Wang, R. R., Wang, Y. Y., & Dai, C. Q. (2022). Influence of higher-order nonlinear effects on optical solitons of the complex Swift–Hohenberg model in the mode-locked fiber laser. Optics & Laser Technology, 152, 108103. doi:10.1016/j.optlastec.2022.108103
   Web of Science ®Google Scholar
• Wen, X., Feng, R., Lin, J., Liu, W., Chen, F., & Yang, Q. (2021). Distorted light bullet in a tapered graded-index waveguide with PT symmetric potentials. Optik, 248, 168092. doi:10.1016/j.ijleo.2021.168092
   Web of Science ®Google Scholar
• Xu, Z., Chen, H., & Dai, Z. (2014). Rogue wave for the (2 + 1)-dimensional Kadomtsev–Petviashvili equation. Applied Mathematics Letters, 37, 34–38. doi:10.1016/j.aml.2014.05.005
   Web of Science ®Google Scholar
• Yel, G., Sulaiman, T. A., & Baskonus, H. M. (2020). On the complex solutions to the (3 + 1)-dimensional conformable fractional modified KdV–Zakharov–Kuznetsov equation. Modern Physics Letters B, 34(05), 2050069. doi:10.1142/S0217984920500694
   Google Scholar
• Yue, C., Khater, M. M., Attia, R. A., & Lu, D. (2020). Computational simulations of the couple Boiti–Leon–Pempinelli (BLP) system and the (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation. AIP Advances, 10(4), 045216. doi:10.1063/1.5142796
   Web of Science ®Google Scholar