Analytical treatments of the space–time fractional coupled nonlinear Schrödinger equations

Lakestanı M., Manafian J.

Optical and Quantum Electronics, cilt.50, sa.11, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 11
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s11082-018-1615-9
  • Dergi Adı: Optical and Quantum Electronics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Conformable time-fractional equations, The exp(-Ω(η))-expansion method, The extended trial equation method, The semi-inverse variational principle method, The space–time fractional coupled nonlinear Schrödinger equations, The tan (ϕ(η) / 2) -expansion method
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Under investigation in this work is a (2 + 1)-dimensional the space–time fractional coupled nonlinear Schrödinger equations, which describes the amplitudes of circularly-polarized waves in a nonlinear optical fiber. With the aid of conformable fractional derivative and the fractional wave transformation, we derive the analytical soliton solutions in the form of rational soliton, periodic soliton, hyperbolic soliton solutions by four integration method, namely, the extended trial equation method, the exp(-Ω(η))-expansion method and the improved tan (ϕ(η) / 2) -expansion method and semi-inverse variational principle method. Based on the the extended trial equation method, we derive the several types of solutions including singular, kink-singular, bright, solitary wave, compacton and elliptic function solutions. Under certain condition, the 1-soliton, bright, singular solutions are driven by semi-inverse variational principle method. Based on the analytical methods, we find that the solutions give birth to the dark solitons, the bright solitons, combine dark-singular, kink, kink-singular solutions with fractional order for nonlinear fractional partial differential equations arise in nonlinear optics.