Solitary and periodic waves of a new kind

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 354, Issue 1713, 1996, Pages 1775-1806

  Benjamin, T B ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MODELLING-MATHEMATICAL; WAVES;

EID: 0029839269     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1996.0078     Document Type: Article

References (32)

1. Adams, R. A. 1975 Sobolev spaces. New York: Academic.
2. Albert, J. P. & Bona, J. L. 1991 Total positivity and the stability of internal waves in stratified fluids of finite depth. IMA J. Appl. Math. 46, 1-19.
3. Amman, H. 1976 Fixed-point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18, 620-709.
4. Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559-592.
5. Benjamin, T. B. 1971 A unified theory of conjugate flows. Phil. Trans. R. Soc. Lond. A 269, 587-592.
6. Benjamin, T. B. 1972 The stability of solitary waves. Proc. R. Soc. Lond. A 328, 153-189.
7. Benjamin, T. B. 1992 A new kind of solitary wave. J. Fluid Mech. 245, 401-411.
8. Benjamin, T. B., Bona, J. L. & Bose, D. K. 1990 Solitary-wave solutions of nonlinear problems. Phil. Trans. R. Soc. Lond. A 331, 195-244.
9. Bona, J. L. 1975 On the stability theory of solitary waves. Proc. R. Soc. Lond. A 344, 363-374.
10. Bona, J. L., Souganidis, P. E. & Strauss, W. A. 1987 Stability and instability of solitary waves of Korteweg-de Vries type. Proc. R. Soc. Lond. A 411, 395-412.
11. Carslaw, H. S. 1921 Introduction to the theory of Fourier's series and integrals, 2nd edn. London: Macmillan.
12. Deimling, K. 1985 Nonlinear functional analysis. Berlin: Springer.
13. Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of integral transforms, vol. 1, New York: McGraw-Hill.
14. Erdélyi, A. 1956 Asymptotic expansions. New York: Dover.
15. Granas, A. 1972 The Leray-Schauder index and fixed point theory for arbitrary A.N.R.s. Bull. Soc. Math. Fr. 100, 209-228.
16. Grillakis, M., Shatah, J. & Strauss, W. A. 1987 Stability theory for solitary waves in the presence of symmetry. J. Funct. Analysis 74, 160-197.
17. Hardy, G. H., Littlewood, J. E. & Polyá, G. 1964 Inequalities, 2nd edn. Cambridge University Press.
18. Hutson, V. & Pym, J. S. 1980 Applications of functional analysis and operator theory. New York: Academic.
19. Jeffreys, H. & Jeffreys, B. S. 1956 Methods of mathematical physics, 3rd edn. Cambridge University Press.
20. Kato, T. 1976 Perturbation theory for linear operators, 2nd edn. Berlin: Springer.
21. Kato, T. 1980 A short introduction to perturbation theory for linear operators. Berlin: Springer.
22. Korteweg, D. J. & de Vries, G. 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Phil. Mag. 39, 422-443.
23. Krasnosel'skii, M. A. 1964 Positive solutions of operator equations. Groningen: Noordhoff.
24. Kreyszig, E. 1978 Introductory functional analysis with applications. New York: Wiley.
25. Lighthill, M. J. 1958 Fourier analysis and generalized functions. Cambridge University Press.
26. Liusternik, L. A. & Sobolev, V. J. 1961 Elements of functional analysis. New York: Ungar.
27. Lloyd, N. G. 1978 Degree theory. Cambridge University Press.
28. Morse, P. M. & Feshbach, H. 1953 Methods of theoretical physics, vol. 1. New York: McGraw Hill.
29. Ono, H. 1975 Algebraic solitary waves in stratified fluids. J. Phys. Soc. Japan 39, 1082-1091.
30. Pego, R. L. & Weinstein, M. I. 1992 Eigenvalues, and instabilities of solitary waves. Phil. Trans. R. Soc. Lond. A. 340, 47-94.
31. Souganidis, P. E. & Strauss, W. A. 1990 Instability of a class of dispersive solitary waves. Proc. R. Soc. Edinb. A 114, 195-212.
32. Smirnov, V. I. 1964 Integration and functional analysis. (A Course of Higher Mathematics 5). Oxford: Pergamon.