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Self-similar regimes of anisotropic collapses

Published online by Cambridge University Press:  09 March 2009

L. Bergé ,
G. Pelletier  and
D. Pesme
L. Bergé
Affiliation:
G.I.L.M.T.-Centre de Physique Atomique de Toulouse U.R.A. 277 du C.N.R.S., Université P. Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France
G. Pelletier
Affiliation:
G.I.L.M.T.-Centre de Physique Atomique de Toulouse U.R.A. 277 du C.N.R.S., Université P. Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France
D. Pesme
Affiliation:
G.I.L.M.T.-Centre de Physique Atomique de Toulouse U.R.A. 277 du C.N.R.S., Université P. Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France
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Abstract

The anisotropic wave collapses governed by the Zakharov equations or by the nonlinear Schrödinger equation are investigated by means of a transformation group exhibiting self-similar anisotropic solutions characterized by two contraction rates. We show the existence of two infinite sets of anisotropic self-similar collapses corresponding, respectively, to “pancake” (oblate) and “cigar” (oblong) shaped collapsing solutions. Both of these classes of anisotropic structures are furthermore shown to be bounded from below by two peculiar solutions whose validity extends from the subsonic to the supersonic regime (the so-called “trans-sonic” solutions) and from above by the standard isotropic solutions. Spatial profiles of trans-sonic anisotropic solutions are analytically derived.

Type
Research Article
Information
Laser and Particle Beams , Volume 9 , Issue 2 , June 1991 , pp. 371 - 379
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Bergé, L. et al. 1991 Laser Part. Beams 9, 373.Google Scholar
Degtyarev, L. M., Zakharov, V. E. & Rudakov, L. I. 1975 Zh. Eksp. Teor. Fiz. 68, 115 [Sov. Phys. JETP 41, 57].Google Scholar
Degtyarev, L. M., Zakharov, V. E. & Rudakov, L. I. 1976 Fiz. Plazmy 2, 438 [Sov. J. Plasma Phys. 2, 240].Google Scholar
Galeev, A. A. et al. 1975 Fiz. Plazmy 1, 438 [Sov. J. Plasma Phys., 1, 5].Google Scholar
Goldman, M. V. 1984 Rev. Mod. Phys. 56, 709.CrossRefGoogle Scholar
Malkin, V. M. & Khudik, V. N. 1987 Zh. Eksp. Teor. Fiz. 92, 2076 [Sov. Phys. JETP 65, 1170].Google Scholar
Newman, D. L., Robinson, P. A. & Goldman, M. V. 1989 Phys. Rev. Lett. 62, 2132.CrossRefGoogle Scholar
Pelletier, G. 1987 Physica D 27, 187.CrossRefGoogle Scholar
Robinson, P. A., Newman, D. L. & Goldman, M.V. 1988 Phys. Rev. Lett. 61, 702.CrossRefGoogle Scholar
Rudakov, L. I. & Tsytovitch, V. N. 1978 Phys. Rep. 40, 1–73.CrossRefGoogle Scholar
Zakharov, V. E. 1972 Zh. Eksp. Teor. Fiz. 62, 1745 [Sov. Phys. JETP 54, 1064].Google Scholar
Zakharov, V. E. & Shur, L. N. 1981 Zh. Eksp. Teor. Fiz. 81, 2019 [Sov. Phys. JETP 54, 1064].Google Scholar