Solitons and other nonlinear waves for stochastic Schrödinger-Hirota model using improved modified extended tanh-function approach. (English) Zbl 1536.35132
Summary: The improved modified extended tanh-function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger-Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.
© 2023 John Wiley & Sons Ltd.
© 2023 John Wiley & Sons Ltd.
MSC:
| 35C08 | Soliton solutions |
| 35R11 | Fractional partial differential equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
improved modified extended tanh-function approach; stochastic Jacobi elliptic solutions; stochastic periodic solutions; stochastic Schrödinger-Hirota equation; stochastic soliton solutions; Wiener processReferences:
| [1] | W.Lyu and Z. A.Wang, Global classical solutions for a class of reaction‐diffusion system with density‐suppressed motility, Electron. Res. Arch.30 (2022), 995-1015. · Zbl 1486.35260 |
| [2] | H.‐Y.Jin and Z.‐A.Wang, Global stabilization of the full attraction‐repulsion Keller‐Segel system, Discret. Contin. Dyn. Syst.40 (2020), 3509-3527. · Zbl 1439.35063 |
| [3] | H.‐Y.Jin and Z.‐A.Wang, Asymptotic dynamics of the one‐dimensional attraction-repulsion Keller-Segel model, Math. Methods Appl. Sci.38 (2015), 444-457. · Zbl 1310.35005 |
| [4] | L.Sun, J.Hou, C.Xing, and Z.Fang, A robust Hammerstein‐Wiener model identification method for highly nonlinear systems, Processes10 (2022), no. 12, 2664. |
| [5] | Z.Peng, J.Hu, K.Shi, R.Luo, R.Huang, B. K.Ghosh, and J.Huang, A novel optimal bipartite consensus control scheme for unknown multi‐agent systems via model‐free reinforcement learning, Appl. Math. Comput.369 (2020), 124821. · Zbl 1433.93008 |
| [6] | B.Zhou, K.Ding, J.Wang, L.Wang, P.Jin, and T.Tang, Experimental study on the interactions between wave groups in double‐wave‐group focusing, Phys. Fluids35 (2023), no. 3, 037118. |
| [7] | B.Zhou, Z.Zheng, Q.Zhang, P.Jin, L.Wang, and D.Ning, Wave attenuation and amplification by an abreast pair of floating parabolic breakwaters, Energy271 (2023), 127077. |
| [8] | H.Chen, M.Liu, Y.Chen, S.Li, and Y.Miao, Nonlinear lamb wave for structural incipient defect detection with sequential probabilistic ratio test, 2022. Security and Communication Networks, 2022. |
| [9] | N.Kadkhoda, E.Lashkarian, M.Inc, M. A.Akinlar, and Y.‐M.Chu, New exact solutions and conservation laws to the fractional‐order Fokker-Planck equations, Symmetry12 (2020), no. 8, 1282. |
| [10] | S.Sahoo, S.Saha Ray, M. A. M.Abdou, M.Inc, and Y.‐M.Chu, New soliton solutions of fractional Jaulent‐Miodek system with symmetry analysis, Symmetry12 (2020), no. 6, 1001. |
| [11] | M. S.Hashemi and M.Mirzazadeh, Optical solitons of the perturbed nonlinear Schrödinger equation using lie symmetry method, Optik281 (2023), 170816. |
| [12] | S.‐W.Yao, S.Gulsen, M. S.Hashemi, M.Inc, and H.Bicer, Periodic Hunter-Saxton equation parametrized by the speed of the Galilean frame: its new solutions, Nucci’s reduction, first integrals and Lie symmetry reduction, Results Phys.47 (2023), 106370. |
| [13] | M. S.Hashemi, A novel approach to find exact solutions of fractional evolution equations with non‐singular kernel derivative, Chaos, Solitons Fract.152 (2021), 111367. · Zbl 1496.35426 |
| [14] | Y.‐M.Chu, M.Inc, M. S.Hashemi, and S.Eshaghi, Analytical treatment of regularized Prabhakar fractional differential equations by invariant subspaces, Comput. Appl. Math.41 (2022), no. 6, 271. · Zbl 1524.35685 |
| [15] | E.Lashkarian and S. R.Hejazi, Exact solutions of the time fractional nonlinear Schrödinger equation with two different methods, Math. Methods Appl. Sci.41 (2018), no. 7, 2664-2672. · Zbl 1391.76655 |
| [16] | A. H.Abdel Kader, M. S.Abdel Latif, and D.Baleanu, Some exact solutions of a variable coefficients fractional biological population model, Math. Methods Appl. Sci.44 (2021), no. 6, 4701-4714. · Zbl 1475.35345 |
| [17] | S.Malik, M. S.Hashemi, S.Kumar, H.Rezazadeh, W.Mahmoud, and M. S.Osman, Application of new Kudryashov method to various nonlinear partial differential equations, Opt. Quantum Electron.55 (2023), no. 1, 8. |
| [18] | M.Tahir, S.Kumar, H.Rehman, M.Ramzan, A.Hasan, and M. S.Osman, Exact traveling wave solutions of Chaffee-Infante equation in (2+1)‐dimensions and dimensionless Zakharov equation, Math. Methods Appl. Sci.44 (2021), no. 2, 1500-1513. · Zbl 1470.35116 |
| [19] | Y.‐M.Chu, M. M. A.Khater, and Y. S.Hamed, Diverse novel analytical and semi‐analytical wave solutions of the generalized (2+1)‐dimensional shallow water waves model, AIP Adv.11 (2021), no. 1, 15223. |
| [20] | H.‐M.Yin, B.Tian, J.Chai, and X.‐Y.Wu, Stochastic soliton solutions for the (2+1)‐dimensional stochastic Broer-Kaup equations in a fluid or plasma, Appl. Math. Lett.82 (2018), 126-131. · Zbl 1393.35186 |
| [21] | S.Khan, Stochastic perturbation of optical solitons with quadratic-cubic nonlinear refractive index, Optik212 (2020), 164706. |
| [22] | S.Khan, A.Biswas, Q.Zhou, S.Adesanya, M.Alfiras, and M.Belic, Stochastic perturbation of optical solitons having anti‐cubic nonlinearity with bandpass filters and multi‐photon absorption, Optik178 (2019), 1120-1124. |
| [23] | S.Khan, F. B.Majid, A.Biswas, Q.Zhou, M.Alfiras, S. P.Moshokoa, and M.Belic, Stochastic perturbation of optical Gaussons with bandpass filters and multi‐photon absorption, Optik178 (2019), 297-300. |
| [24] | A. G.Hossam, H.Abd‐Allah, and M.Zakarya, Exact solutions of stochastic fractional Korteweg de‐Vries equation with conformable derivatives, Chinese Phys. B29 (2020), no. 3, 30203-030203. |
| [25] | E. M. E.Zayed, R. M. A.Shohib, M. E. M.Alngar, K. A.Gepreel, T. A.Nofal, and Y.Yıldırım, Optical solitons for Biswas-Arshed equation with multiplicative noise via itô calculus using three integration algorithms, Optik258 (2022), 168847. |
| [26] | A. H.Soliman and A.‐A.Hyder, Closed‐form solutions of stochastic KdV equation with generalized conformable derivatives, Physica Scripta95 (2020), no. 6, 65219. |
| [27] | T.Han, Z.Li, K.Shi, and G.‐C.Wu, Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers, Chaos, Solitons Fract.163 (2022), 112548. · Zbl 1507.35353 |
| [28] | Z.Korpinar, F.Tchier, M. Inc, and A. A.Alorini, On exact solutions for the stochastic time fractional Gardner equation, Phys. Scripta95 (2020), no. 4, 45221. |
| [29] | A.‐A.Hyder and A. H.Soliman, Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators, Math. Methods Appl. Sci.45 (2022), no. 14, 8600-8612. · Zbl 1528.60066 |
| [30] | G.‐Z.Wu and C.‐Q.Dai, Nonautonomous soliton solutions of variable‐coefficient fractional nonlinear Schrödinger equation, Appl. Math. Lett.106 (2020), 106365. · Zbl 1442.35531 |
| [31] | T.He and Y.‐Y.Wang, Dark‐multi‐soliton and soliton molecule solutions of stochastic nonlinear Schrödinger equation in the white noise space, Appl. Math. Lett.121 (2021), 107405. · Zbl 1489.35253 |
| [32] | C.Chen, J.Hong, L.Ji, and L.Kong, A compact scheme for coupled stochastic nonlinear Schrödinger equations, Commun. Comput. Phys.21 (2017), no. 1, 93-125. · Zbl 1373.60108 |
| [33] | F.Abdolabadi, A.Zakeri, and A.Amiraslani, A charge‐preserving compact splitting method for solving the coupled stochastic nonlinear Schrödinger equations, Appl. Numer. Math.181 (2022), 293-319. · Zbl 1504.35462 |
| [34] | Y. F.Alharbi, M. A.Sohaly, and M. A. E.Abdelrahman, Fundamental solutions to the stochastic perturbed nonlinear Schrödinger’s equation via gamma distribution, Results Phys.25 (2021), 104249. |
| [35] | A.Tikan, Effect of local peregrine soliton emergence on statistics of random waves in the one‐dimensional focusing nonlinear Schrödinger equation, Phys. Rev. E101 (2020), no. 1, 12209. |
| [36] | D. S.Cargill, R. O.Moore, and C. J.McKinstrie, Noise bandwidth dependence of soliton phase in simulations of stochastic nonlinear Schrödinger equations, Opt. Lett.36 (2011), no. 9, 1659-1661. |
| [37] | E. M. E.Zayed, R. M. A.Shohib, M. E. M.Alngar, A.Biswas, L.Moraru, S.Khan, Y.Yıldırım, H. M.Alshehri, and M. R.Belic, Dispersive optical solitons with Schrödinger-Hirota model having multiplicative white noise via Itô calculus, Phys. Lett. A445 (2022), 128268. · Zbl 1498.81073 |
| [38] | Z.Yang and B. Y. C.Hon, An improved modified extended tanh‐function method, Zeitschrift für Naturforschung A61 (2006), no. 3‐4, 103-115. · Zbl 1186.35195 |
| [39] | A.Darwish, H. M.Ahmed, A. H.Arnous, and M. F.Shehab, Optical solitons of Biswas-Arshed equation in birefringent fibers using improved modified extended tanh‐function method, Optik227 (2021), 165385. |
| [40] | A.Darwish, A. R.Seadawy, H. M.Ahmed, A. L.Elbably, M. F.Shehab, and A. H.Arnous, Study on soliton solutions of the longitudinal wave equation and magneto‐electro‐elastic circular rod dynamical model, Int. J. Modern Phys. B35 (2021), no. 13, 2150168. · Zbl 1465.35367 |
| [41] | M. F.Shehab, M. M. A.El‐Sheikh, A. A. G.Mabrouk, and H. M.Ahmed, Dynamical behavior of solitons with Kudryashov’s quintuple power‐law of refractive index having nonlinear chromatic dispersion using improved modified extended tanh‐function method, Optik266 (2022), 169592. |
| [42] | Y.Chu, M. A.Shallal, S. M.Mirhosseini‐Alizamini, H.Rezazadeh, S.Javeed, and D.Baleanu, Application of modified extended tanh technique for solving complex Ginzburg‐Landau equation considering Kerr law nonlinearity, Comput., Mater. Contin.66 (2021), no. 2, 1369-1377. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
