2009/09/30 by E. V. Ferapontov, K. R. Khusnutdinova, К. Р. Хуснутдинова +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #math.AP #nlin.SI
paper · pdf · doi:10.48550/arxiv.0909.5685
36 pages, 19 figures. Added solutions via a Jacobi inversion problem on hyperellitic surfaces, humplike solutions and reduction to the KdV equation
openalex publication_date 2009/09/30 · arxiv created 2010/03/09 · arxiv updated 2010/03/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We investigate (d+1)-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case d≥ 3 we formulate a conjecture that any such system with an irreducible dispersion relation must be linearly degenerate. We prove this conjecture in the 2-component case, providing a complete classification of multi-dimensional integrable systems in question. In particular, our results imply the non-existence of 2-component integrable systems of hydrodynamic type for d≥ 6. In the second half of the paper we discuss a numerical and analytical evidence for the impossibility of the breakdown of smooth initial data for linearly degenerate systems in 2+1 dimensions.