Construction of a Blow-Up Solution for the Complex Ginzburg–Landau Equation in a Critical Case
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DOI: 10.1007/s00205-017-1211-3
Abstract: We construct a solution for the Complex Ginzburg–Landau equation in a critical case which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. The… read more here.
Keywords: solution complex; complex ginzburg; ginzburg landau; equation critical ... See more keywords
The Landau Equation with the Specular Reflection Boundary Condition
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DOI: 10.1007/s00205-020-01496-5
Abstract: The existence and stability of the Landau equation (1936) in a general bounded domain with a physical boundary condition is a long-outstanding open problem. This work proves the global stability of the Landau equation with… read more here.
Keywords: reflection boundary; boundary condition; specular reflection; equation ... See more keywords
Reduction of a Tri-Modal Lorenz Model of Ferrofluid Convection to a Cubic–Quintic Ginzburg–Landau Equation Using the Center Manifold Theorem
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DOI: 10.1007/s12591-021-00565-9
Abstract: The differential geometric method of the center manifold theorem is applied to the magnetic-Lorenz model of ferrofluid convection in an electrically non-conducting ferrofluid. The analytically intractable tri-modal nonlinear autonomous system (magnetic-Lorenz model) is reduced to… read more here.
Keywords: landau equation; ginzburg landau; lorenz model; equation ... See more keywords
The Gelfand–Shilov smoothing effect for the radially symmetric homogeneous Landau equation with Shubin initial datum
Sign Up to like & getrecommendations! Published in 2018 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2018.04.022
Abstract: Abstract In this paper, we study the Cauchy problem associated with the radially symmetric spatially homogeneous non-cutoff Landau equation with Maxwellian molecules, while the initial datum belongs to negative-index Shubin space, which can be characterized… read more here.
Keywords: smoothing effect; gelfand shilov; radially symmetric; initial datum ... See more keywords
Dark-singular combo optical solitons with fractional complex Ginzburg-Landau equation
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DOI: 10.1016/j.ijleo.2018.06.076
Abstract: Abstract This paper employs dextended Jacobi's elliptic function expansion method to retrieve doubly periodic function as solutions to the stochastic complex Ginzburg–Landau equation. In the limiting case, when the modulus of ellipticity approaches unity, these… read more here.
Keywords: complex ginzburg; ginzburg landau; optical solitons; singular combo ... See more keywords
Entropy dissipation estimates for the relativistic Landau equation, and applications
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DOI: 10.1016/j.jfa.2019.04.007
Abstract: Abstract In this paper we study the Cauchy problem for the spatially homogeneous relativistic Landau equation with Coulomb interactions. Despite its physical importance, this equation has not received a lot of mathematical attention we think… read more here.
Keywords: relativistic landau; entropy dissipation; equation; dissipation estimates ... See more keywords
The local and global existence of solutions for a time fractional complex Ginzburg–Landau equation
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DOI: 10.1016/j.jmaa.2018.08.008
Abstract: Abstract We study the following time fractional complex nonlinear Ginzburg–Landau equation: { e − i ω 0 C D t α u − △ u = e i γ | u | p − 1… read more here.
Keywords: ginzburg landau; landau equation; time fractional; fractional complex ... See more keywords
Recurrent motion in the fractional complex Ginzburg–Landau equation
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DOI: 10.1063/1.5131376
Abstract: This article concerns recurrent motion in the fractional complex Ginzburg–Landau equation with a small recurrent force. By using Galerkin’s method and energy estimate method, we obtain the existence of the bounded solutions, periodic solutions, quasiperiodic… read more here.
Keywords: fractional complex; motion fractional; complex ginzburg; ginzburg landau ... See more keywords
Infinitely many multi-vortex solutions of the magnetic Ginzburg–Landau equation with external potentials in R2
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DOI: 10.1063/5.0028065
Abstract: In this paper, we consider the magnetic Ginzburg–Landau equation with external potentials μV(x) for the type II superconductors. We prove, by reduction arguments, that under suitable conditions on V(x), the magnetic Ginzburg–Landau equation with external… read more here.
Keywords: ginzburg landau; magnetic ginzburg; external potentials; landau equation ... See more keywords
The Study of the Numerical Treatment of the Real Ginzburg–Landau Equation Using the Galerkin Method
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DOI: 10.1080/01630563.2021.1948863
Abstract: Abstract The real Ginzburg–Landau equation is studied in this article. We proceed and use the Galerkin method in combination with the compactness theorem to show that the solution of this problem exists and is unique… read more here.
Keywords: ginzburg landau; galerkin method; landau equation; real ginzburg ... See more keywords
Random attractor of stochastic complex Ginzburg–Landau equation with multiplicative noise on unbounded domain
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DOI: 10.1080/07362994.2016.1259075
Abstract: ABSTRACT The existence of a compact random attractor for the stochastic complex Ginzburg–Landau equation with multiplicative noise has been investigated on unbounded domain. The solutions are considered in suitable spaces with weights. According to crucial… read more here.
Keywords: complex ginzburg; ginzburg landau; stochastic complex; random attractor ... See more keywords