About a scalar Lax-type representation for a class of hydrodynamic systems in one dimension (Q2754788)
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scientific article; zbMATH DE number 1668414
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | About a scalar Lax-type representation for a class of hydrodynamic systems in one dimension |
scientific article; zbMATH DE number 1668414 |
Statements
4 November 2001
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hydrodynamic system
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Lax-type representation
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finite-dimensional reduction
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surface evolution
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0.86895686
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0.85800457
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0.8552245
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0.85298586
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0.8526139
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About a scalar Lax-type representation for a class of hydrodynamic systems in one dimension (English)
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It is proved that a wide class of hydrodynamic system possesses a homogeneous scalar representation of the Lax type. Basing on the Novikov-Bogoyavlenskij technique of finite-dimensional reductions, existence of quasi-soliton solutions for studied hydrodynamic systems is established. Using numerical and analytical methods, a system having application in fluid dynamics is considered. This system, describing surface evolution of thin film jets and fluid sheets, has the form \(u_t=h_{xxx}-u_x u\), \(h_t=-(uh)_x\) and is a natural generalization of the well-known Burgers flow, possessing both dissipative and soliton-like solutions.
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