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Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint. (English) Zbl 1070.35029

Summary: We study the explicit homoclinic orbits solutions for the “bad” Boussinesq equation with periodic boundary condition and even constraint, and periodic soliton solutions for the “good” Boussinesq equation with even constraint.

MSC:

35Q35 PDEs in connection with fluid mechanics
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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References:

[1] Zakharov, V. E., Collapse of langmuir waves, Sov Phys JETP, 35, 908-912 (1972)
[2] Ablowitz, M. J.; Hernst, B. M., SIAM J Appl Math, 50, 339 (1990) · Zbl 0707.35141
[3] Ercolani, N.; Forest, M. G.; Mclaughlin:, D. W., Phys D, 43, 349 (1990) · Zbl 0705.58026
[4] Ablowitz, M. J.; Herbst, B. M.; Schober, C. M., J Comput Phys, 126, 299 (1996) · Zbl 0866.65064
[5] Herbst, B. M.; Ablowitz, M. J.; Ryan, E., Comput Phys Commun, 65, 137 (1991) · Zbl 0900.65350
[6] Mckean, H. P., Common Pure Appl Math, XXXIV, 599-691 (1981) · Zbl 0473.35070
[7] Hirota, R., Phys Rev Lett, 27, 1192 (1971) · Zbl 1168.35423
[8] Hirota R, Satsuma J. 2000;53(3):283-99; Hirota R, Satsuma J. 2000;53(3):283-99
[9] Bona, J. L.; Sachs, R. L., Commun Math Phys, 118, 15-29 (1988) · Zbl 0654.35018
[10] Weiss, J., J Math Phys, 26, 258-269 (1985) · Zbl 0565.35103
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