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Optical solitons with generalized quadratic–cubic nonlinearity



  1. Department of Physics, Diamond Harbour Women’s University, D. H. Road, Sarisha–743368, West Bengal, India
  2. Department of Mathematics and Physics, Grambling State University, Grambling, LA—71245, USA
  3. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah–21589, Saudi Arabia
  4. Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati—800201, Romania
  5. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa
  6. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow–115409, Russian Federation
  7. Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey


This work obtains soliton solutions to the governing nonlinear Schrödinger’s equation by traveling wave hypothesis. The model is considered with the generalized quadratic–cubic nonlinearity that is also a special case of Kudryashov’s form of nonlinear refractive index setting the coefficients of nonlinear terms with negative exponents, in Kudryashov’s nonlinearity, to zero. Based on the sign of the discriminant, plane waves, bright or singular solitons emerge. Notably, a major shortcoming of this approach is that traveling waves fail to recover dark optical solitons to the model. Thus, traveling wave hypothesis has its own limitations just as various other integrability approaches which has their own shortcomings–a strong message as this paper conveys. The parameter constraints for the existence of these solitons and plane waves are also presented..


Solitons, Quadratic–cubic, Traveling waves.


JAYITA DAN, SUDIP GARAI, A. GHOSE-CHOUDHURY, ANJAN BISWAS, YAKUP YILDIRIM, HASHIM M. ALSHEHRI, Optical solitons with generalized quadratic–cubic nonlinearity, Optoelectronics and Advanced Materials - Rapid Communications, 16, 9-10, September-October 2022, pp.450-452 (2022).

Submitted at: Feb. 3, 2022

Accepted at: Oct. 5, 2022