Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation
K. Hosseini, Mohammad Mirzazadeh, M.S. Osman, Maysaa Al Qurashi, Dumitru Bǎleanu
Abstract
The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg–Landau equation.
Topics & Concepts
Elliptic functionSolitonJacobi elliptic functionsElliptic integralFunction (biology)Theta functionWork (physics)Mathematical analysisMathematical physicsPhysicsMathematicsQuantum mechanicsNonlinear systemBiologyEvolutionary biologyNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Fiber Laser Technologies