Fractional optical solitons with stochastic properties of a wick-type stochastic fractional NLSE driven by the Brownian motion

References

• Yepez-Martinez H, Gomez-Aguilar JF. Fractional sub-equation method for Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative. Waves Random Complex Media. 2019;29:678–693.
   Web of Science ®Google Scholar
• Fei J, Cao W. Explicit soliton-cnoidal wave interaction solutions for the (2 + 1)-dimensional negative-order breaking soliton equation. Waves Random Complex Media. 2020;30:54–64.
   Web of Science ®Google Scholar
• Li PF, Li RJ, Dai CQ. Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction. Opt Express. 2021;29:3193–3209.
   PubMed Web of Science ®Google Scholar
• Dai CQ, Wang YY. Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals. Nonlinear Dyn. 2020;102:1733–1741.
   Web of Science ®Google Scholar
• Yu LJ, Wu GZ, Wang YY, et al. Traveling wave solutions constructed by Mittag-Leffler function of a (2 + 1)-dimensional space-time fractional NLS equation. Results Phys. 2020;17:103156.
   Google Scholar
• Wang BH, Lu PH, Dai CQ, et al. Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas-Lenells equation. Alex Eng J. 2020;59:4699–4707.
   Web of Science ®Google Scholar
• Dai CQ, Wang YY, Zhang JF. Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials. Nonlinear Dyn. 2020;102:379–391.
   Web of Science ®Google Scholar
• Hashemi MS, Akgul A. Solitary wave solutions of time–space nonlinear fractional Schrodinger’s equation: two analytical approaches. J Comput Appl Math. 2018;339:147–160.
   Web of Science ®Google Scholar
• Wu GZ, Yu LJ, Wang YY. Fractional optical solitons of the space–time fractional nonlinear Schrodinger equation. Optik. 2020;207:164405.
   Web of Science ®Google Scholar
• Lan Z, Guo B. Nonlinear waves behaviors for a coupled generalized nonlinear Schrödinger–Boussinesq system in a homogeneous magnetized plasma. Nonlinear Dyn. 2020;100:3771–3784.
   Web of Science ®Google Scholar
• Wabnitz S, Wetzel B. Instability and noise-induced thermalization of Fermi-Pasta-Ulam recurrence in the nonlinear Schrödinger equation. Phys Lett A. 2014;378:2750–2756.
   Web of Science ®Google Scholar
• Zeng L, Zeng J. One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential. Nonlinear Dyn. 2019;98:985–995.
   Web of Science ®Google Scholar
• Lu PH, Wang BH, Dai CQ. Fractional traveling wave solutions of the (2 + 1)-dimensional fractional complex Ginzburg–Landau equation via two methods. Math Meth Appl Sci. 2020;43:8518–8526.
   Web of Science ®Google Scholar
• Abdel-Salam EAB, Mourad MF. Fractional quasi AKNS-technique for nonlinear space-time fractional evolution equations. Math Meth Appl Sci. 2019;42:5953–5968.
   Web of Science ®Google Scholar
• Chen YX, Ou-Yang FY. Excitation management of crossed Akhmediev and Ma breather for a nonautonomous partially nonlocal Gross-Pitaevskii equation with an external potential. Nonlinear Dyn. 2020;100:1543–1550.
   Web of Science ®Google Scholar
• Wazwaz AM, Xu GQ. Kadomtsev–Petviashvili hierarchy: two integrable equations with time-dependent coefficients. Nonlinear Dyn. 2020;100:3711–3716.
   Web of Science ®Google Scholar
• Liu CS. Counterexamples on Jumarie’s three basic fractional calculus formulae for non-differentiable continuous functions. Chaos Solit Fractals. 2018;109:219–222.
   Web of Science ®Google Scholar
• El-Sayed AMA, Yousif EA, El-Aasser MA. Analytical solution of the space-time fractional nonlinear Schrödinger equation. Rep Math Phys. 2016;77:19–34.
   Web of Science ®Google Scholar
• Wang BH, Lu PH, Dai CQ, et al. Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrodinger equation. Results Phys. 2020;17:103036.
   Web of Science ®Google Scholar
• Dai CQ, Zhang JF. Stochastic exact solutions and two-soliton solution of the wick-type stochastic KdV equation. EPL. 2009;86:40006.
   Web of Science ®Google Scholar
• Chen B, Xie YC. Periodic-like solutions of variable coefficient and wick-type stochastic NLS equations. J Comput Appl Math. 2007;203:249–263.
   Web of Science ®Google Scholar
• Wills AC. Analysis of regularity and convergence of discretization methods for the stochastic heat equation forced by space-time white noise. Dissertations & Theses Gradworks. 2015.
   Google Scholar
• Holden H, Øksendal B, Ubøe J, et al. Stochastic partial differential equations. Birkhauser; 1996.
   Google Scholar
• Ghany HA, Mohammed MS. White noise functional solutions for wick-type stochastic fractional KdV-Burgers-Kuramoto equations. Chin J Phys. 2012;12:619–627.
   Google Scholar
• Li X, Gu J, Xu W, et al. Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations. Nonlinear Dyn. 2018;93:1579–1588.
   Web of Science ®Google Scholar
• Bass FG, Kivshar YS, Konotop VV, et al. On stochastic dynamics of solitons in inhomogeneous optical fibers. Opt Commun. 1989;70:309–314.
   Web of Science ®Google Scholar
• Liu Z, Zhang H, Yan J, et al. A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise. Appl Math Lett. 2019;98:419–426.
   Web of Science ®Google Scholar
• Xu P, Zou G, Huang J. Time–space fractional stochastic Ginzburg–Landau equation driven by fractional Brownian motion. Comput Math Appl. 2019;78:3790–3806.
   Web of Science ®Google Scholar
• Korpinar Z, Tchier F, Inc M, et al. Applicability of time conformable derivative to Wick-fractional-stochastic PDEs. Alex Eng J. 2020;59:1485–1493.
   Web of Science ®Google Scholar
• Wu GZ, Dai CQ. Nonautonomous soliton solutions of variable-coefficient fractional nonlinear Schrödinger equation. Appl Math Lett. 2020;106:106365.
   Web of Science ®Google Scholar
• Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput Math Appl. 2006;51:1367–1376.
   Web of Science ®Google Scholar
• Chen YX, Xiao X, Mei ZL. Optical soliton solutions of the (1 + 1)-dimensional space-time fractional single and coupled nonlinear Schrödinger equations. Results Phys. 2020;18:103211.
   Web of Science ®Google Scholar
• He JH, Elagan SK, Li ZB. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus. Phys Lett A. 2012;376:257–259.
   Web of Science ®Google Scholar
• Wazwaz AM, Kaur L. Complex simplified Hirota’s forms and Lie symmetry analysis for multiple real and complex soliton solutions of the modified KdV–Sine-Gordon equation. Nonlinear Dyn. 2019;95:2209–2215.
   Web of Science ®Google Scholar
• Abdelrahman MAE, Sohaly MA, Moaaz O. The deterministic and stochastic solutions of the NLEEs in mathematical physics. Int J Appl Comput Math. 2019;5:40.
   Google Scholar
• Wick GC. The evaluation of the collision matrix. Phys Rev. 1950;80:268–272.
   Web of Science ®Google Scholar
• Xie Y. Exact solutions of the wick-type stochastic Kadomtsev–Petviashvili equations. Chaos Solit Fractals. 2004;21:473–480.
   Web of Science ®Google Scholar
• Lorenz EN. Deterministic nonperiodic flow. J Atmos Sci. 1963;20:130–141.
   Web of Science ®Google Scholar
• Ma ZY, Hu YH. Solitons, chaos and fractals in the (2 + 1)-dimensional dispersive long wave equation. Chaos Solit Fractals. 2007;34:1667–1676.
   Web of Science ®Google Scholar
• Clerc M, Coullet P, Tirapegui E. Lorenz bifurcation: instabilities in quasireversible systems. Phys Rev Lett. 1999;83:3820–3823.
   Web of Science ®Google Scholar
• Yang RC, Hao RY, Li L, et al. Exact gray multi-soliton solutions for nonlinear Schrödinger equation with variable coefficients. Opt Commun. 2005;253:177–185.
   Web of Science ®Google Scholar
• Wang JF, Li L, Jia ST. Exact chirped gray soliton solutions of the nonlinear Schrödinger equation with variable coefficients. Opt Commun. 2007;274:223–230.
   Web of Science ®Google Scholar
• Wang BH, Wang YY. Fractional white noise functional soliton solutions of a WICK-type stochastic fractional NLSE. Appl Math Lett. 2020;110:106583.
   Web of Science ®Google Scholar