Bifurcation analysis and exact solutions for a class of generalized time-space fractional nonlinear Schrodinger equations

被引:2
作者
Hong, Baojian [1 ]
机构
[1] Nanjing Inst Technol, Fac Math Phys, Nanjing 211167, Peoples R China
关键词
time-space fractional nonlinear Schrodinger equation; general mapping deformation method; Caputo fractional derivative; bifurcation; exact solutions; EXACT SOLITARY WAVE; COMPLEX TRANSFORM; CALCULUS;
D O I
10.3934/mbe.2023643
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this work, we focus on a class of generalized time-space fractional nonlinear Schrodinger equations arising in mathematical physics. After utilizing the general mapping deformation method and theory of planar dynamical systems with the aid of symbolic computation, abundant new exact complex doubly periodic solutions, solitary wave solutions and rational function solutions are obtained. Some of them are found for the first time and can be degenerated to trigonometric function solutions. Furthermore, by applying the bifurcation theory method, the periodic wave solutions and traveling wave solutions with the corresponding phase orbits are easily obtained. Moreover, some numerical simulations of these solutions are portrayed, showing the novelty and visibility of the dynamical structure and propagation behavior of this model.
引用
收藏
页码:14377 / 14394
页数:18
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  • [1] THE FRACTIONAL COMPLEX TRANSFORM: A NOVEL APPROACH TO THE TIME-FRACTIONAL SCHRoDINGER EQUATION
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  • [2] Exact solitary wave solutions of the complex nonlinear Schrodinger equations
    Arbabi, Somayeh
    Najafi, Mohammad
    [J]. OPTIK, 2016, 127 (11): : 4682 - 4688
  • [3] Numerically absorbing boundary conditions for quantum evolution equations
    Arnold, A
    [J]. VLSI DESIGN, 1998, 6 (1-4) : 313 - 319
  • [4] Exact solutions to the (2 thorn 1)-Dimensional Heisenberg ferromagnetic spin chain equation by using modified simple equation and improve F-expansion methods
    Bashar, Md Habibul
    Islam, S. M. Rayhanul
    [J]. PHYSICS OPEN, 2020, 5
  • [5] The fractional-order governing equation of Levy motion
    Benson, DA
    Wheatcraft, SW
    Meerschaert, MM
    [J]. WATER RESOURCES RESEARCH, 2000, 36 (06) : 1413 - 1423
  • [6] Prediction and dynamical evolution of multipole soliton families in fractional Schrodinger equation with the PT-symmetric potential and saturable nonlinearity
    Bo, Wen-Bo
    Wang, Ru-Ru
    Fang, Yin
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    [J]. NONLINEAR DYNAMICS, 2023, 111 (02) : 1577 - 1588
  • [7] Optical soliton solutions of the (1+1)-dimensional space-time fractional single and coupled nonlinear Schrodinger equations
    Chen, Yi-Xiang
    Xiao, Xiao
    Mei, Zhen-Lin
    [J]. RESULTS IN PHYSICS, 2020, 18
  • [8] An invariant set in energy space for supercritical NLS in 1D
    Cuccagna, Scipio
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 352 (02) : 634 - 644
  • [9] THE PIECEWISE REPRODUCING KERNEL METHOD FOR THE TIME VARIABLE FRACTIONAL ORDER ADVECTION-REACTION-DIFFUSION EQUATIONS
    Dai, Dan-Dan
    Ban, Ting-Ting
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    [J]. THERMAL SCIENCE, 2021, 25 (02): : 1261 - 1268
  • [10] Conformable space-time fractional nonlinear (1+1)-dimensional Schrodinger-type models and their traveling wave solutions
    Darvishi, M. T.
    Najafi, Mohammad
    Wazwaz, Abdul-Majid
    [J]. CHAOS SOLITONS & FRACTALS, 2021, 150