Hydrodynamic reductions and solutions of a universal hierarchy

Theoretical and Mathematical Physics

Volumn 140, Issue 2, 2004, Pages 1073-1085

  Alonso, L Martínez ^a   Shabat, A B ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

Differential reductions; Hodograph solutions; Hydrodynamic systems

Indexed keywords

EID: 22044442966     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:TAMP.0000036538.41884.57     Document Type: Article

References (18)

1. L. Martínez Alonso and A. B. Shabat, Phys. Lett. A, 300, 58 (2002).
2. L. Martínez Alonso and A. B. Shabat, J. Nonlinear Math. Phys., 10, 229 (2003);
3. "On the prolongation of a hierarchy of hydrodynamic chains," in: New Trends in Integrability and Partial Solvability (NATO Sci. Ser., Vol. 132, A. B. Shabat et al., eds.), Kluwer, Dordrecht, p. 263.
4. A. B. Shabat, Theor. Math. Phys., 136, 1066 (2003).
5. V. G. Mikhalev, Funct. Anal. Appl., 26, 140 (1992).
6. M. Jaulent and I. Miodek, Lett. Math. Phys., 1, 243 (1976);
7. Lett. Nuovo Cimento, 20, 655 (1977);
8. L. Martínez Alonso, J. Math. Phys., 21, 2342 (1980);
9. M. Antonowicz and A. P. Fordy, Phys. D, 28, 345 (1987);
10. A. N. W. Hone, Phys. Lett. A, 249, 46 (1998).
11. R. Camassa and D. Holm, Phys. Rev. Lett., 71, 1661 (1993).
12. J. Gibbons and Y. Kodama, Phys. Lett. A, 135, 167 (1989);
13. J. Gibbons and S. P. Tsarev, Phys. Lett. A, 211, 19 (1996);
14. J. Gibbons and S. P. Tsarev, Phys. Lett. A, 258, 263 (1999);
15. M. Mañas, L. Martínez Alonso, and E. Medina, J. Phys. A, 35, 401 (2002).
16. E. V. Ferapontov and K. R. Khusnutdinova, "On integrability of (2+1)-dimensional quasilinear systems," nlin.SI/0305044 (2003).
17. M. V. Pavlov, "Integrable hydrodynamic chains," nlin.SI/0301010 (2003).
18. S. P. Tsarev, Izv. Akad. Nauk USSR, Ser. Mat., 37, 397 (1991).