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| Content Provider | Springer Nature Link |
|---|---|
| Author | Zykov, S. A. El, G. A. Kamchatv, A. M. Pavlov, M. V. |
| Copyright Year | 2010 |
| Abstract | We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component ‘cold-gas’ hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the ‘cold-gas’ component densities and construct a number of exact solutions having special properties (quasiperiodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows. |
| Ending Page | 191 |
| Page Count | 41 |
| Starting Page | 151 |
| File Format | |
| ISSN | 09388974 |
| e-ISSN | 14321467 |
| Journal | Journal of Nonlinear Science |
| Issue Number | 2 |
| Volume Number | 21 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2010-09-17 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Soliton gas Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) ApplicationMathematics/Computational Methods of Engineering Integrability Theoretical, Mathematical and Computational Physics Nonlinear first-order hyperbolic equations Soliton theory, asymptotic behavior of solutions Hydrodynamic reduction Analysis Thermodynamic limit Kinetic equation Mechanics Economic Theory |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Engineering Modeling and Simulation |
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