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Conservation laws for cubic–quartic optical solitons with complex Ginzburg–Landau equation having five nonlinear refractive index structures

ANJAN BISWAS1,2,3,4,5,* , ABDUL H. KARA6, SALAM KHAN5, YAKUP YIDIRIM7, M. F. MAHMOOD8, HASHIM M. ALSHEHRI2, MILIVOJ R. BELIC9

Affiliation

  1. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow–115409, Russian Federation
  2. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah–21589, Saudi Arabia
  3. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa
  4. Department of Applied Sciences, Cross–Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati–800201, Romania
  5. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762–4900, USA
  6. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits–2050, Johannesburg, South Africa
  7. Department of Mathematics, Faculty of Arts and Sciences, Near East University, 99138 Nicosia, Cyprus
  8. Department of Mathematics, Howard University, Washington, DC–20059, USA
  9. Institute of Physics Belgrade, Pregrevica 118, 11080 Zemun, Serbia

Abstract

This paper recovers and exhibits the conservation law for cubic–quartic complex Ginzburg–Landau model which are considered with five nonlinear forms. The Hamiltonian, linear momentum and the power are derived, save one. For parabolic–nonlocal law, the Hamiltonian and the linear momentum are not retrievable by Lie symmetry.

Keywords

Cubic–quartic solitons, Conservation laws, Ginzburg–Landau equation.

Citation

ANJAN BISWAS, ABDUL H. KARA, SALAM KHAN, YAKUP YIDIRIM, M. F. MAHMOOD, HASHIM M. ALSHEHRI, MILIVOJ R. BELIC, Conservation laws for cubic–quartic optical solitons with complex Ginzburg–Landau equation having five nonlinear refractive index structures, Optoelectronics and Advanced Materials - Rapid Communications, 16, 3-4, March-April 2022, pp.137-141 (2022).

Submitted at: Aug. 21, 2021

Accepted at: April 7, 2022