Explicit optical dromions with Kerr law having fractional temporal evolution

Gangwei Wang, Qin Zhou*, Ali Saleh Alshomrani, Anjan Biswas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this work, we derived the (2+1)-dimensional Schrödinger equation from the (2+1)-dimensional Klein-Gordon equation. We also obtained the fractional order form of this equation at the same time so as to discover the connection between them. For the (2+1)-dimensional Klein-Gordon equation, symmetries and conservation laws are pres ented. For different gauge constraint, from the perspective of conservation laws, the corresponding symmetries are obtained. After that, based on the fractional complex transform, soliton solutions of the time fractional (2+1)-dimensional Schrödinger equation are displayed. Some figures are showed behaviors of soliton solutions. It is important to discover the relationships between these equations and to obtain their explicit solutions. These solutions will perhaps provide a theoretical basis for the explanation of complex nonlinear phenomena. From the results of this paper, it is clear that the Lie symmetry method is a particularly important tool for dealing with differential equations.

Original languageEnglish
Article number2350056
Issue number5
Publication statusPublished - 8 Jul 2023
Externally publishedYes


  • (2+1)-Dimensional Klein-Gordon Equation
  • Nonlinear Schrödinger Equation
  • Perturbation Analysis
  • Soliton Solutions


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