Binary modulated oscillations in a semi-discrete version of Burgers equation

Physica D: Nonlinear Phenomena

Volumn 106, Issue 3-4, 1997, Pages 287-313

  Hayes, Brian T ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; INTEGRATION; NUMERICAL ANALYSIS;

BINARY MODULATED EQUATIONS; BURGER EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS;

OSCILLATIONS;

EID: 0031210302     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00044-4     Document Type: Article

References (20)

1. A.M. Bloch and Y. Kodaraa, Dispersive regularization of the Whithara equation for the Toda lattice, SIAM J. Appl. Math. 52 (1992) 909-928.
2. G.F. Carrier, M. Krook and C.E. Pearson, Functions of a Complex Variable (Hod Books, Ithaca, New York, 1983).
3. R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves, Applied Mathematical Science Series, Vol. 21 (Springer, New York, 1976).
4. H. Flaschka, The Toda lattice I. Existence of integrals, Phys. Rev. B 9 (1973) 1924-1925.
5. J. Goodman and P.D. Lax, On dispersive difference schemes I, Comm. Pure Appl. Math. 41 (1988) 1-25.
6. J.M. Greenberg, The shock generation problem for a discrete gas with short range repulsive force, Comm. Pure Appl. Math. 45 (1992) 1125-1139.
7. B.T. Hayes, Studies of the Kac-van Moerbeke Lattice, Ph.D. Dissertation, New York University Graduate School of Arts and Science (May 1994).
8. B.L. Holian, H. Flaschka and D.W. McLaughlin, Shock waves in the Toda lattice: Analysis, Phys. Rev. A 24 (1981) 2595-2623.
9. T.Y. Hou and P.D. Lax, Dispersive approximations in fluid dynamics, Comm. Pure Appl. Math. 44 (1991) 1-40.
10. M. Kac and P. van Moerbeke, On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices, Adva.in Math. 16 (1975) 160-169.
11. P.D. Lax and C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation I, II, and III, Comm. Pure Appl. Math. 36 (1983) 253-290, 571-593, 809-829.
12. P.D. Lax, C.D. Levermore and S. Venakides, The generation and propagation of oscillations in dispersive IVP's and their limiting behavior, in: Important Developments in Soliton Theory 1980-1990, eds. T. Fokas and V.E. Zakharov (Springer, Berlin, 1992).
13. C.D. Levermore and J.G. Liu, Large oscillations arising in a dispersive numerical scheme, Physica D (1996) 191-216.
14. K.D. T.-R. McLaughlin, A continuum limit of the Toda lattice, Ph.D. Dissertation, New York University Graduate School of Arts and Science (August 1994).
15. P.D. Miller, N.M. Ercolani and C.D. Levermore, Modulation of multiphase waves in the presence of resonance, Physica D 92 (1996) 1-27.
16. J. Moser, Three integrable Hamiltonian systems connected with isospectral deformations, Adv. in Math. 16 (1975) 197-220.
17. R.R. Rosales and C.V. Turner, The small dispersion limit for a non-linear semi-discrete system of equations: Part I, preprint (1995).
18. P. Rosenau and J.M. Hyman, Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70 (1992) 564-567.
19. S. Venakides, P. Deift and R. Oba, The Toda shock problem, Comm. Pure Appl. Math. 44 (1991) 1041-1117.
20. N.J. Zabusky and M.D. Kruskal, Interactions of 'solitons' in a collisionless plasma and recurrence of initial states, Phys. Rev. Lett. 15 (1965) 240-243.