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Two-dimensional algebraic solitary wave and its vertical structure in stratified fluid. (English) Zbl 1170.76318


MSC:

76B25 Solitary waves for incompressible inviscid fluids
76B70 Stratification effects in inviscid fluids
76B65 Rossby waves (MSC2010)
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References:

[1] Benjamin T B. Internal waves of permanent form in fluids of great depth [J]. J Fluid Mech, 1967,29:559–592. · Zbl 0147.46502
[2] Ono H. Algebraic solitary waves in stratified fluids[J]. J Phys Soc Japan, 1975,39(4): 1082–1092. · Zbl 1334.76027
[3] Cheng Youliang, Dai Shiqiang. Second-order internal solitary waves in stratified fluid with great depth [A]. In: Zhou Liandi, Shao Wei wen, Lu Chuanjing, et al. (eds). Proceedings of the 5 th National Conference on Hydrodynamics and the 15 th National Symposium on Hydrodynamics[C]. China Ocean Press, Beijing,2001,53–60 (in Chinese).
[4] Zhang Linghai. Generalized third-order Benjamin-Ono equation [J]. Acta Physica Mathematica Sinica, 1993,13(4):473–479 (in Chinese).
[5] Han Xiaoxiao, Hao Hailong. Decaying property of solutions for higher-order Benjamin-Ono equation[J]. Annals of Mathematics, Ser A, 1996,17(2):163–172 (in Cinese). · Zbl 0862.45012
[6] Zhang Hongqing, Zhang Yufeng. Backlund transformation, nonlinear superposition formula and infinite conserved laws of Benjamin equation [J]. Applied Mathematics and Mechanics (English Edition), 2001,22(10),1127–1131. · Zbl 0994.35110 · doi:10.1007/BF02436448
[7] Grimshaw R, Zhu Y. Oblique interaction between internal solitary waves [J]. Stud Appl Math, 1994,92:249–270. · Zbl 0813.76091
[8] Ablowitz M J, Segur H. Long internal waves in fluids of great depth [J]. Stud Appl Math, 1980,62:249–262. · Zbl 0447.76013
[9] Tsuji H. Oblique interaction of internal solitary waves in a two-layer fluid of infinite depth [J]. Fluid Dynamics Research,2001,29:251–267. · Zbl 1075.76519
[10] Lighthill J. Waves in Fluid[M]. Cambridge University Press, Cambridge, 1978. · Zbl 0375.76001
[11] Shen Guoguang, Li Deyun. Ray theory and trapped waves in study of internal waves [J]. Journal of Hydrodynamics, Ser A, 1996,11 (1):43–51 (in Chinese).
[12] Broutman D, Rottman J W, Eckermann S D. Ray methods for internal waves in the atmosphere and ocean[J]. Annu Rev Fluid Mech,2004,34:559–593. · Zbl 1076.76018
[13] Laksshmih Kantha, Carolanne Clayson. Small Scale Processes in Geophysical Fluid Flows [M]. Academic Press, New York, 2000. · Zbl 0989.76002
[14] Yih C S. Fluid Mechanics[M]. Zhang Keben,Zhang Diming,Lu Qiqiang (transls). Higher Education Press, Beijing, 1983 (Chinese version).
[15] Tominaga. Ocean Waves[M]. Guan Mengru (transl). Science Press, Beijing, 1984 (Chinese version).
[16] Dai Shiqiang. Reductive perturbation method and analyses of far fields of nonlinear waves [J]. Advances in Mechanics, 1982,12(1):2–23 (in Chinese).
[17] Guo Dunren. Methods of Mathematical Physics[M]. People’s Education Press, Beijing, 1965 (in Chinese).
[18] Li Jiachun, Zhou Xianchu. Asymptotic Methods in Mathematical Physics[M]. Science Press, Beijing, 1998 (in Chinese).
[19] Xu Zhaoting. Dynamics of Internal Waves in Oceans [M]. Science Press, Beijing, 1999 (in Chinese).
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