دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات44
تعداد شماره‌ها1,321
تعداد مقالات16,203
تعداد مشاهده مقاله52,831,561
تعداد دریافت فایل اصل مقاله15,507,775
Bagheri, Majid, Khani, Ali. (1401). Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative. سامانه مدیریت نشریات علمی, 10(2), 549-566. doi: 10.22034/cmde.2021.40523.1766
Majid Bagheri; Ali Khani. "Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative". سامانه مدیریت نشریات علمی, 10, 2, 1401, 549-566. doi: 10.22034/cmde.2021.40523.1766
Bagheri, Majid, Khani, Ali. (1401). 'Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative', سامانه مدیریت نشریات علمی, 10(2), pp. 549-566. doi: 10.22034/cmde.2021.40523.1766
Bagheri, Majid, Khani, Ali. Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative. سامانه مدیریت نشریات علمی, 1401; 10(2): 549-566. doi: 10.22034/cmde.2021.40523.1766

Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative

Computational Methods for Differential Equations
مقاله 20، دوره 10، شماره 2، تیر 2022، صفحه 549-566    اصل مقاله (443.62 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.40523.1766
نویسندگان
Majid Bagheri؛ Ali Khani*
Faculty of Science, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
چکیده
In this article, a new version of the trial equation method is suggested. This method allows new exact solutions of the nonlinear partial differential equations. The developed method is applied to unstable nonlinear fractionalorder Schrödinger equation in fractional time derivative form of order α. Some exact solutions of the fractionalorder fractional PDE are attained by employing the new powerful expansion approach using by beta-fractional derivatives which are used to get many solitary wave solutions by changing various parameters. New exact solutions are expressed with rational hyperbolic function solutions, rational trigonometric function solutions, 1-soliton solutions, dark soliton solitons, and rational function solutions. We can say that unstable nonlinear Schrödinger equation exist different dynamical behaviors. In addition, the physical behaviors of these new exact solutions are given with two and three dimensional graphs.
کلیدواژه‌ها
Unstable nonlinear fractional-order Schrödinger equation؛ Beta-fractional derivative؛ New powerful expansion approach؛ Nonlinear partial differential equations
مراجع
  • [1]          S. Abbasbandy and A. Shirzadi, The first integral method for modified Benjamin-Bona-Mahony equation, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 1759-1764.
  • [2]          M. A. Abdou, Further improved F-expansion and new exact solutions for nonlinear evolution equations, Nonlinear Dyn., 52 (2008), 277-288.
  • [3]          M. A. Akbar,  N. H. M. Ali,  and S. T. Mohyud-Din,  The  modified  alternative  G’/G-expansion  method  to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel’d-Sokolov-Wilson  equation,  Springer Plus, 327 (2013), 2-16.
  • [4]          M. N. Alam, Exact solutions to the foam drainage equation by using the new generalized  G’/G-expansion  method, Results Phys., 5 (2015), 168-177.
  • [5]          M. N. Alam and M. A. Akbar, Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G’/G)-expansion method, J. Egyptian Math. Soc., 22 (2014), 402-406.
  • [6]          M. N. Alam, M. A. Akbar, and M. F. Houque, Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation using the new approach of gener- alized (G’/G)-expansion method, Pramana, 83 (2014), 317-329.
  • [7]          M. N. Alam and M. M. Alam, An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules, J. Taibah Univ. Sci., 11 (2017), 939-948.
  • [8]          M. N. Alam and X. Li, Exact traveling wave solutions to higher order nonlinear equations, J. Ocean Eng. Sci., 4 (2019), 276-288.
  • [9]          M. N. Alam and X. Li, New soliton solutions to the nonlinear complex fractional Schrodinger equation and     the conformable time-fractional Klein-Gordon equation with quadratic and cubic nonlinearity, Phys. Scr., 95 (2020), 045224.
  • [10]        M. N. Alam and C. Tunç, The new solitary wave structures for the (2 + 1)-dimensional time-fractional Schrodinger equation and the space-time nonlinear conformable  fractional  Bogoyavlenskii  equations, Alexan- dria Eng. J., 59 (2020), 2221-2232.
  • [11]        S. Arbabi and M. Najafi, Exact solitary wave solutions of the complex nonlinear Schrödinger equations, Optik., 127 (2016), 4682-4688.
  • [12]        A. Atangana and D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel, Theory and application to heat transfer model, Therm Sci., 20 (2016), 763-769.
  • [13]        A. Atangana and I. Koca, Chaos in a simple nonlinear system with Atangana-Baleanu derivative with fractional order, Chaos Solitons Frac., 89 (2016), 447-454.
  • [14]        H. M. Baskonus, A. Kumar, A. Kumar, and W. Gao, Deeper investigations of the (4+1)-dimensional Fokas and (2+1)-dimensional Breaking soliton equations, Int. J. Modern Phys. B, 34 (2020) 2050152.
  • [15]        S. T. Demiray, Y. Pandir, and H. Bulut, New solitary wave solutions of Maccari system, Ocean Eng., 103 (2015), 153-159.
  • [16]        S. T. Demiray, Y. Pandir, and H. Bulut, New soliton solutions for Sasa-Satsuma equation, Waves Random Complex Media, 25 (3) (2015), 417-428.
  • [17]        Z. Fu, S. Liu and Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear  wave equations, Phys. Lett. A., 290 (2001), 72-76.
  • [18]        W. Gao, G. Yel, H. M. Baskonus, and C. Cattani, Complex Solitons in the Conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur Equation, Aims Math., 5 (2020), 507-521.
  • [19]        J. L. G. Guirao, H. M. Baskonus and A. Kumar, Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order, Math., 8 (2020), 341.
  • [20]        S. Guo and and Y. Zhou, The extended G’/G-expansion method and its applications to the Whitham- Broer-Kaup like equations and coupled Hirota-Satsuma KdV equations, Appl. Math. Comput., 215 (2010), 3214-3221.
  • [21]        Y. Gurefe, E. Misirli, A. Sonmezoglu, and M. Ekici, Extended trial equation method to generalized nonlinear partial differential equations, Appl. Math. Comput., 219 (2013), 5253-5260.
  • [22]        Y. Gurefe, A. Sonmezoglu, and E. Misirl, Application of an irrational trial equation method to high dimen- sional nonlinear evolution equations, J. Adv. Math. Stud., 5 (2012), 41-47.
  • [23]        Y. Gurefe, A. Sonmezoglu, and E. Misirl, Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics, Pramana-J. Phys., 77 (2011), 1023-1029.
  • [24]        J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Frac., 30 (2006), 700-708.
  • [25]        J. Hietarinta, Hirota’s bilinear method and its generalization, Int. J. Mod. Phys. A., 12 (1997), 43-51.
  • [26]        K. Hosseini, M. Samavat, M. Mirzazadeh, W. X. Ma, and Z. Hammouch, A New (3+1)-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions, Regular Chaotic Dyn., 25 (2020), 383-391.
  • [27]        A. Houwe, J. Sabi’u, Z. Hammouch, and S. Y. Doka, Solitary pulses of a conformable nonlinear differential equation governing wave propagation in low-pass electrical transmission line, Phys. Scr., 5 (2020), 4027-4044.
  • [28]        E. Ilhan and I. O. Kiymaz, A generalization of truncated M-fractional derivative and applications to fractional differential equations, Appl. Math. Nonlinear Sci., 5 (2020), 171-188.
  • [29]        H. F. Ismael, H. Bulut, H. M. Baskonus, and W. Gao, Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis, Commun. Theo. Phys., 72 (2020), 115002 (8pp).
  • [30]        X. J. Laia, J. F. Zhang, and S. H. Mei, Application of the Weierstrass elliptic expansion method to the long-wave and short-wave resonance interaction system, Z. Naturforsch., 63a (2008), 273-279.
  • [31]        D. Lu, A. R. Seadawy and A. Ali, Structure of traveling wave solutions for some nonlinear models via modified mathematical method, Open Phys., 16 (2018), 854-860.
  • [32]        C. S. Liu, A new trial equation method and its applications, Commun. Theor. Phys., 45 (2006), 395-397.
  • [33]        C. S. Liu, Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations, Commun. The. Phys., 181 ( 2010), 317-324.
  • [34]        C. S. Liu, Trial equation method and its applications to nonlinear evolution equations, Phys. Sinica, 54 (2005), 2505-2509.
  • [35]        C. S. Liu, Using trial equation to solve the exact solutions for two kinds of KdV  equations  with  variable coeffients, Acta Phys. Sinica, 54 (2005), 4506-4510.
  • [36]        D. Lu, A. R. Seadawy, and M. Arshad, Bright-dark solitary wave and elliptic function solutions of unstable nonlinear Schrodinger equation and their applications, Opt. Quant. Elec., 50 (2018), 1-10.
  • [37]        C. S. Liu, Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications, Commun. The. Phys., 45 (2006), 219-223.
  • [38]        W. X. Ma and B. Fuchssteiner, Explicit and exact solutions to a Kolmogrov- Petrovski-Piskunov equation, Int. J. Nonlinear Mech., 31 (1996), 329-338.
  • [39]        W. Malfliet, The tanh method:  a tool  for solving certain classes of nonlinear evolution and wave equations,       J. Comput. Appl. Math., 164 -165 (2004), 529-541.
  • [40]        W. Malfliet and W. Hereman, The tanh method: I exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54 (1996), 563-568.
  • [41]        Y. Pandir, A new type of the generalized F-expansion method and its  application  to  Sine-Gordon  equation, Celal Bayar Univ. J. Sci., 13 (2017), 647-650.
  • [42]        Y. Pandir, Symmetric fibonacci function solutions of some nonlinear partial  differential  equations,  Appl.  Math. Inf. Sci., 8 (2014), 2237-2241.
  • [43]        Y. Pandir, S. T. Demiray, and H. Bulut, A new approach for some NLDEs with variable coefficients, Optik., 127 (2016), 11183-11190.
  • [44]        Y. Pandir, Y. Gurefe, U. Kadak, and E. Misirli, Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution, Abst. Appl. Anal., 2012 (2012), ID 478531.
  • [45]        Y. Pandir, Y. Gurefe, and E. Misirli, Classification of exact solutions to the generalized Kadomtsev- Petviashvili equation, Phys. Scr., 87 (2013), 025003.
  • [46]        Y. Pandir, Y. Gurefe, and E. Misirli, A multiple extended trial equation method for the fractional Sharma- Tasso-Olver equation, AIP Conf. Proc., 1558 (2013), 1927.
  • [47]        Y. Pandir, A. Sonmezoglu, H. H. Duzgun, and N.Turhan, Exact solutions of nonlinear Schrodinger’s equation by using generalized Kudryashov method, AIP Conf. Proc., 1648 (2015), 370004.
  • [48]        Y. Pandir and N. Turhan, A new version of the generalized F-expansion method and its applications, AIP Conf. Proc., 1798 (2017), 020122.
  • [49]        O. Pashaev and G. Tanoglu, Vector shock soliton and the Hirota bilinear method, Chaos Solitons Frac., 26 (2005) 95-105.
  • [50]        L. K. Rav, S. S. Ray, and S. Sahoo, New exact solutions of coupled Boussinesq-Burgers equations by exp- function method, J. Ocean Eng. Sci., 2 (2017), 34-46.
  • [51]        K.M. Saad, A. Atangana, and D. Baleanu, New fractional derivatives with non-singular kernel applied to the burgers equation, Chaos, 28 (2018), 63-109.
  • [52]        M. Shakee and S. T. Mohyud-Din, New G’/G-expansion method and its application to the Zakharov- Kuznetsov- VBenjamin-Bona-Mahony (ZK- VBBM) equation, J. Association Arab Uni. Basic Appl. Sci., 18 (2015), 66-81.
  • [53]        S. Shen and Z. Pan, A note on the Jacobi elliptic function expansion method, Phys. Lett. A., 308 (2003), 143-148.
  • [54]        R. Silambarasan, H. M. Baskonus, R. V. Anand, M. Dinakaran, B. Balusamy, and W. Gao, Longitudinal strain waves propagating in an infinitely long  cylindrical  rod  composed  of  generally  incompressible  materials and its Jacobi elliptic function solutions, Math. Comput. Simul., 182 (2021), 566-602.
  • [55]        Y. A. Tandogan, Y. Pandir, and Y. Gurefe, Solutions of the nonlinear differential equations by use of modified Kudryashov method, Turkish J. Math. Comput. Sci., 1 (2013), 54-60.
  • [56]        E. T. Tebue, Z.I. Djoufack, E. F. Donfack, A. K. Jiotsa, and T. C. Konfane, Exact solutions of the unstable nonlinear Schrödinger equation with the new Jacobi elliptic function rational expansion method and  the  exponential rational function method, Optik, 127 (2016), 11124-11130.
  • [57]        M. Wang and X. Li, Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation, Chaos Solitons Frac., 24 (2005), 1257-1268.
  • [58]        K. Yang and J. Liu, The extended F-expansion method and exact solutions of nonlinear PDEs, Chaos Solitons Frac., 22 (2004), 111-121.
  • [59]        G. Yel, H. M. Baskonus, and W. Gao, New dark-bright soliton in the shallow water wave model, AIMS Math., 5 (2020) 4027-4044.
  • [60]        J. Zhang, F. Jiang, and X. Zhaok, An improved an improved (G’/G)-expansion method for solving nonlinear evolution equations, Int. J. Comput. Math., 87 (2010), 1716-1725.
آمار
تعداد مشاهده مقاله: 719
تعداد دریافت فایل اصل مقاله: 760


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب