The main idea of this study is to obtain the soliton-type solutions conformable time-fractional complex Ginzburg–Landau equation with Kerr law nonlinearity. For aim, generalized and modified Kudryashov methods are applied given model. reason for using a derivative that chain rule can be derivative. Thus, suitable wave transform, converted into an ordinary differential equation. Then, proposed r...

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equ...

Several systems discussed at this workshop on Spatio-Temporal Patterns in Nonequilibrium Complex Systems have been related to or analyzed in the context of the so-called Complex Ginzburg-Landau equation (CGL). What is the difference between the physics underlying the usual amplitude description for stationary patterns and the one underlying the CGL? Why are there many more stable coherent struc...

Complex Ginzburg-Landau Equations were originated in the theory of Super-conductivity, 13]. When Ginzburg-Landau parameter chosen to be a special constant, the equations are called self-dual vortex equations that were carefully studied by Jaae and Taubes 16]. For the vortex equation on a Riemannian surface , one considers an open, smooth domain with, possibly empty, smooth boundary @. Let L be ...

Suppose that ω ⊂ Ω ⊂ R. In the annular domain A = Ω \ ω̄ we consider the class J of complex valued maps having degree 1 on ∂Ω and ∂ω. It was conjectured in [5] that the existence of minimizers of the Ginzburg-Landau energy Eκ in J is completely determined by the value of the H-capacity cap(A) of the domain and the value of the Ginzburg-Landau parameter κ. The existence of minimizers of Eκ for al...

The symmetries and conserved quantities of Manton's modified superconductiv-ity model with non-relativistic Maxwell-Chern-Simons dynamics (also related to the Quan-tized Hall Effect) are obtained in the " Kaluza-Klein type " framework of Duval et al. 1. Introduction Recently [1], Manton proposed a modified version of the Landau-Ginzburg theory of superconductivity. His equations, defined on (2 ...