On the non-uniqueness of nonlinear wave solutions in a viscous layer (Q1064209)
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scientific article; zbMATH DE number 3920061
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the non-uniqueness of nonlinear wave solutions in a viscous layer |
scientific article; zbMATH DE number 3920061 |
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On the non-uniqueness of nonlinear wave solutions in a viscous layer (English)
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1985
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Solutions of the stationary travelling wave type are considered in draining layers of a viscous fluid. A one-parameter family of waves is studied that softly branches off into the upper branch of the neutral stability curve of the plane-parallel flow and goes over into a negative soliton (phase velocity \(c<3)\) as the wave number tends to zero. It is shown that this family is not unique: for small values of the parameter \(\delta\) characterizing the mass flow rate, a second and third family of waves branches off from it with half the period.
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bifurcation
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positive soliton
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linear asymptotic forms
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stationary travelling wave
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draining layers of a viscous fluid
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one-parameter family of waves
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neutral stability curve
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negative soliton
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