Long-wave-short-wave interaction in bubbly liquids †

Journal of Applied Mathematics and Mechanics

Volumn 63, Issue 6, 1999, Pages 917-926

  Akhatov, I Sh ^a   Khismatullin, D B ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033234415     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(00)00009-5     Document Type: Article

References (21)

1. Korteveg, D. J. and de Vries, G., On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves. Phil. Mag., 1985, 5, 39, 422-443.
2. Gardner, C. S. and Morikawa, G. K., Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves. New York University, Courant Inst. Math. Sci., Res. Rep. TID-6184, 1960.
3. Hasimoto, H. and Ono, H., Nonlinear modulation of gravity waves. J. Phys. Soc. Japan, 1972, 33, 3, 805-811.
4. Zakharov, V. E., The collapse of Langmuir waves. Zh. Eksper. Teor. Fiz., 1972, 62, 5,
5. Benney, D. J., Significant interactions between small and large scale surface waves. Stud. Appl. Math. 1976, 55,2,93-106.
6. Benney, D. J., A general theory for interactions between short and long waves. Stud. Appl. Math. 1977, 56, 1, 81-94.
7. Djordjevic, V. D. and Redekopp, L. G., On two-dimensional packets of capillary gravity waves. J. Fluid Mech., 1977, 79, 4, 703-714.
8. Davydov, A. S., Solitons in molecular systems. Phys. Scr., 1979, 20, 3-4, 387-394.
9. Nigmatulin, R. I., The Dynamics of Media, Part 1. Nauka, Moscow, 1987.
10. Wijngaarden, L. van., On the equations of motion for mixtures of liquid and gas bubbles. J. Fluid. Mech., 1968, 33, 465-474.
11. Nakoryakov, V. Ye., Pokusayev, B. G. and Shreiber, I. R., Wave Propagation in Gas- and vapour-liquid media. Inst. Teplofiziki, Sib. Otd. Akad. Nauk SSSR, Novosibirsk, 1983.
12. Gumerov, N. A., On quasimonochromatic weakly non-linear waves in a bubbly medium with a small dissipation. Prikl. Mat. Mekh., 1992, 56, 1, 58-67.
13. Gavrilyuk, S. L., Modulation equations for a bubbly medium with an incompressible carrier phase. Zh. Prikl. Mekh. Tekh. Fiz., 1989, 2, 86-92.
14. Gumerov, N. A., Equations describing the propagation of nonlinear modulation waves in bubbly liquids. Bubble Dynamics and Interface Phenomena. Kluwer Academic, Dordrecht, 1994, 131-140.
15. Zabolotskaya, Ye. A., Non-linear waves in a liquid with gas bubbles. Trudy Inst. Obshch. Fiz., Akad. Nauk SSSR, 1989, 18, 121-155.
16. Naugol'nykh, K. A. and Ostrovskii, L. A., Non-linear Wave Processes in Acoustics. Nauka, Moscow, 1990.
17. Iordanskii, S. V, On the equations of motion of a liquid containing gas bubbles. Zh. Prikl. Mekh. Tekh. Fiz., 1960, 3, 102-110.
18. Kedrinskii, V. K., Propagation of perturbations in a liquid containing gas bubbles. Zh. Prikl. Mekh. Tekh. Fiz., 1968, 4, 29-34.
19. Jeffrey, A. and Kawahara, T., Asymptotic Methods in Nonlinear Wave Theory. Pitman, London, 1982., 256.
20. Berezin, Yu. A., Numerical Investigation of Non-linear Waves in a Rarefied Plasma. Nauka, Novosibirsk, 1977.
21. Ma, Y.-C, The complete solution of the long-wave-short-wave resonance equations. Stud. Appl. Math., 1978,59,3,201-221.