Fractal modification of complex Ginzburg–Landau model arising in the oscillating phenomena
Yasir Khan
Abstract
The complex Ginzburg-Landau Equation (CGLE) is one of the non-trivial models for addressing the dynamics of oscillating, highly nonlinear processes right before the start of oscillations. This paper presents the complex Ginzburg-Landau fractal model with three types of nonlinearity. The variational approach provides soliton solutions for the CGLE in terms of Kerr, parabolic, and quadratic laws of nonlinearity. New bright and dark soliton solutions for the CGLE are developed. The necessary novel conditions that guarantee the existence of suitable solitary waves are introduced. Monitoring solutions 3D and 2D plots are illustrated by choosing a range of appropriate values of parameters.
Topics & Concepts
FractalNonlinear systemSolitonQuadratic equationPhysicsStatistical physicsRange (aeronautics)MathematicsClassical mechanicsMathematical analysisQuantum mechanicsGeometryMaterials scienceComposite materialNonlinear Dynamics and Pattern FormationFractional Differential Equations SolutionsNonlinear Waves and Solitons