Psi-series solution of fractional Ginzburg–Landau equation
نویسنده
چکیده
One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α with polynomial nonlinearity of order s have the noninteger power-like behaviour of order α/(1 − s) near the singularity. PACS numbers: 05.45.−a, 45.10.Hj
منابع مشابه
Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
متن کاملSome new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملThe Solution of Fractional Nonlinear Ginzburg–landau Equation with Weak Initial Data
In this paper, we study the solution of the fractional nonlinear Ginzburg-Landau(FNGL) equation with weak initial data in the weighted Lebesgue spaces. The existence of a solution to this equation is proved by the contraction-mapping principle.
متن کاملFractional Ginzburg–Landau equation for fractal media
We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equatio...
متن کاملOn elliptic solutions of the cubic complex one-dimensional Ginzburg–Landau equation
The cubic complex one-dimensional Ginzburg–Landau equation is considered. Using the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave no elliptic travelling wave solution. This result amplifies the Hone’s result, that this equation has no elliptic travelling wave solution.
متن کامل