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Modulation equations near the Eckhaus boundary - The KdV equation
[report]
2018
We are interested in the description of small modulations in time and space of wave-train solutions to the complex Ginzburg-Landau equation $\partial_T\Psi=(1+i\alpha)\partial^2_X\Psi+\Psi-(1+i\beta)\Psi|\Psi|^2$ near the Eckhaus boundary, that is, when the wave train is near the threshold of its first instability. Depending on the parameters α, β a number of modulation equations can be derived, such as the KdV equation, the Cahn-Hilliard equation, and a family of Ginzburg-Landau based
doi:10.5445/ir/1000085447
fatcat:pik3rkbrpjbcbmuc3zuekahyda