Abstract
This study delves into investigating the stability of solutions pertaining to the generalized Davey–Stewartson (\({{\mathbb {D}}}{{\mathbb {S}}}\)) equation by employing the generalized rational method and projective Riccati equations method within the Hamiltonian system framework. The central focus lies in unraveling the physical significance of this model within the realm of plasma physics, shedding light on its intricate connections with analogous equations. The generalized \({{\mathbb {D}}}{{\mathbb {S}}}\) equation, a pivotal nonlinear evolution model, serves as a vital tool in comprehending the evolution of coupled waves across various physical systems, notably within the domains of fluid dynamics and plasma physics. Its significance lies in its capacity to elucidate the intricate interplay among different wave components, offering a holistic perspective on wave interactions within plasma mediums. Through the meticulous application of rigorous analytical methods, this investigation uncovers pivotal insights into the stability of solutions, thereby enriching our understanding of mathematical models in plasma physics. The findings presented in this research contribute significantly to advancing the understanding of nonlinear dynamics, with profound implications for future exploration in plasma physics and related fields. In essence, this study underscores the analytical prowess of the generalized rational and projective Riccati equations methods, accentuating their relevance and applicability to the generalized \({{\mathbb {D}}}{{\mathbb {S}}}\) equation and, by extension, their role in enhancing our comprehension of coupled wave phenomena within diverse plasma systems.
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References
Aderyani, S.R., Saadati, R., Vahidi, J.: Multiple exp-function method to solve the nonlinear space-time fractional partial differential symmetric regularized long wave (SRLW) equation and the (1+1)-dimensional Benjamin-Ono equation. Int. J. Mod. Phys. B 37(22), 2350213 (2023)
Ahmad, I., Jalil, A., Ullah, A., Ahmad, S., De la Sen, M.: Some new exact solutions of (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili equation. Results Phys. 45, 106240 (2023)
Akram, U., Seadawy, A.R., Rizvi, S.T.R., Younis, M., Althobaiti, A.: Some new dispersive dromions and integrability analysis for the Davey–Stewartson (DS-II) model in fluid dynamics. Mod. Phys. Lett. B 36(2), 2150539 (2022)
Al-Askar, F.M., Cesarano, C., Mohammed, W.W.: Multiplicative Brownian motion stabilizes the exact stochastic solutions of the Davey–Stewartson equations. Symmetry 14(10), 2176 (2022)
Behera, S.: Analysis of traveling wave solutions of two space-time nonlinear fractional differential equations by the first-integral method. Mod. Phys. Lett. B 38(4), 2350247–390 (2024)
Cao, J., Lu, H.: Exact traveling wave solutions of the generalized Davey–Stewartson equation. J. Shanghai Norm. Univ 44, 330 (2015)
Coppini, F., Grinevich, P.G., Santini, P.M.: The periodic N breather anomalous wave solution of the Davey–Stewartson equations; first appearance, recurrence, and blow up properties. J. Phys. A Math. General 57(1), 015208 (2024)
Dhiman, S.K., Kumar, S.: An optimal system, invariant solutions, conservation laws, and complete classification of Lie group symmetries for a generalized (2+1)-dimensional Davey–Stewartson system of equations for the wave propagation in water of finite depth. Eur. Phys. J. Plus 138(3), 195 (2023)
Ehrnström, M., Groves, M.D., Nilsson, D.: Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation (2021). arXiv:2110.03971
Feng, B., Zhang, Y., Zhang, H.: Applications of the R-matrix method in integrable systems. Symmetry 15(9), 1623 (2023)
Grinevich, P.G., Santini, P.M.: The finite-gap method and the periodic Cauchy problem for (2+1)-dimensional anomalous waves for the focusing Davey–Stewartson 2 equation. Russ. Math. Surv. 77(6), 1029–1059 (2022)
Guo, L., Kevrekidis, P.G., He, J.: Asymptotic dynamics of higher-order lumps in the Davey–Stewartson II equation. J. Phys. A Math. General 55(47), 475701 (2022)
Guo, B., Fang, Y., Dong, H.: Time-fractional Davey–Stewartson equation: Lie point symmetries, similarity reductions, conservation laws and traveling wave solutions. Commun. Theor. Phys. 75(10), 105002 (2023a)
Guo, L., Zhu, M., He, J.: Asymptotic analysis of the higher-order lump in the Davey–Stewartson I equation. J. Math. Phys. 64(12), 123505 (2023b)
Khater, M.M.: Abundant accurate solitonic water and ionic liquid wave structures of the nanoparticle hybrid system. Comput. Appl. Math. 41(4), 177 (2022)
Khater, M.M.A.: Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson–Pickering equation. Results Phys. 44, 106193 (2023a)
Khater, M.M.A.: Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation. Int. J. Geom. Methods Mod. Phys. 20(9), 2350159–12 (2023b)
Khater, M.M.A.: Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation. Heliyon 9, e13511 (2023c)
Khater, M.M.A.: Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos Solitons Fractals 167, 113098 (2023d)
Khater, M.M.A.: Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation. Heliyon 9, e13511 (2023)
Khater, M.M.A.: Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos Solitons Fractals 167, 113098 (2023e)
Khater, M.M., Alfalqi, S.H., Alzaidi, J.F., Attia, R.A.: Computational and numerical simulations; the generalized (2+ 1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation. Results Phys. 52, 106876 (2023f)
Klein, C., Sjöstrand, J., Stoilov, N.: Large \(|k|\) behavior for the reflection coefficient for Davey–Stewartson II equations (2022). arXiv:2203.14650
Kourakis, I., Singh, K., Mc Kerr, M.: Dust-ion acoustic dromions in magnetospheric dusty plasma. In: AGU Fall Meeting Abstracts, vol. 2022, pp. SM32A–61 (2022)
Li, Y.-Y., Zhou, Z.-X.: Dromion solutions of PT-symmetric (x, y)-nonlocal Davey–Stewartson I equation. Commun. Nonlinear Sci. Numer. Simul. 103, 105967 (2021)
Li, L., Zhu, M., Zheng, H., Xie, Y.: Non-compatible partially PT symmetric Davey–Stewartson system: rational and semi-rational solution with nonzero background. Chaos Solitons Fractals 170, 113362 (2023)
Liu, C., Li, Z.: Multiplicative Brownian motion stabilizes traveling wave solutions and dynamical behavior analysis of the stochastic Davey–Stewartson equations. Results Phys. 53, 106941 (2023)
Shi, Z., Huang, G.: Matter-wave dromions in a disk-shaped dipolar Bose–Einstein condensate with the Lee–Huang–Yang correction. Phys. Rev. E 107(2), 024214 (2023)
Singh, K., Kourakis, I., McKerr, M.: Two-dimensional modulated dust-ion-acoustic waves in the presence of a kappa-distributed electron background. In: 44th COSPAR Scientific Assembly. Held 16–24 July, Vol. 44, p. 1229 (2022)
Taimanov, I.A.: The Moutard transformation for the Davey-Stewartson II equation and its geometrical meaning (2021). arXiv:2111.07251
Taimanov, I.A.: On a formation of singularities of solutions to soliton equations represented by L,A,B-triples (2022a). arXiv:2207.04707
Taimanov, I.A.: Surfaces via spinors and soliton equations (2022b). arXiv:2207.07856
Zhang, Y., Liu, H., Wang, L., Sun, W.: The line rogue wave solutions of the nonlocal Davey–Stewartson I equation with PT symmetry based on the improved physics-informed neural network. Chaos 33(1), 013118 (2023)
Acknowledgements
The research work was funded by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R399), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445). The authors are thankful to the Deanship of Graduate Studies and Scientific Research at University of Bisha for supporting this work through the Fast-Track Research Support Program.
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The research work was funded by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R399), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
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Altuijri, R., Abdel-Aty, AH., Nisar, K.S. et al. Unraveling plasma dynamics: stability analysis of generalized \({{\mathbb {D}}}{{\mathbb {S}}}\) equation solutions. Opt Quant Electron 56, 953 (2024). https://doi.org/10.1007/s11082-024-06796-8
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DOI: https://doi.org/10.1007/s11082-024-06796-8