Internal Undular Bores in the Coastal Ocean
39
11. Grimshaw, R. (2010). Transcritical flow past an obstacle. ANZIAM Journal, 52, 1–25.
12. Grimshaw, R. (2015). Change of polarity for periodic waves in the variable-coefficient
Korteweg-de Vries equation. Studies in Applied Mathematics, 134, 363–371.
13. Grimshaw, R. H. J., & Smyth, N. F. (1986). Resonant flow of a stratified fluid over topography.
Journal of Fluid Mechanics, 169, 429–464.
14. Grimshaw, R., Pelinovsky, E., & Talipova, T. (2007). Modeling internal solitary waves in the
coastal ocean. Surveys in Geophysics, 28, 273–298.
15. Grimshaw, R., Pelinovsky, E., Talipova, T., & Kurkina, A. (2010). Internal solitary waves:
Propagation, deformation and disintegration. Nonlinear Processes in Geophysics, 17, 633–
649.
16. Grimshaw, R., & Yuan, C. (2016). The propagation of internal undular bores over variable
topography. Physica D, 333, 200–207.
17. Grimshaw, R., & Yuan, C. (2016). Depression and elevation tsunami waves in the framework
of the Korteweg-de Vries equation. Natural Hazards, 84, S493–S511.
18. Gurevich, A. V., & Pitaevskii, L. P. (1974). Nonstationary structure of a collisionless shock
wave. Soviet Physics JETP, 38, 291–297.
19. Helfrich, K. R., & Melville, W. K. (2006). Long nonlinear internal waves. Annual Review of
Fluid Mechanics, 38, 395–425.
20. Holloway, P., Pelinovsky, E., & Talipova, T. (2001). Internal tide transformation and oceanic
internal solitary waves. In R. Grimshaw (Ed.), Environmental stratified flows (pp. 31–60).
Boston: Kluwer.
21. Kamchatnov, A. M. (2000). Nonlinear periodic waves and their modulations. An introductory
course. World Scientific.
22. Kamchatnov, A. M. (2004). On Whitham theory for perturbed integrable equations. Physica
D, 188, 247–281.
23. Liu, Z., Grimshaw, R., & Johnson, E. (2017). Internal solitary waves propagating through variable background hydrology and currents. Ocean Modelling.
24. Myint, S., & Grimshaw, R. (1995). The modulation of nonlinear periodic wavetrains by dissipative terms in the Korteweg-de Vries equation. Wave Motion, 22, 215–238.
25. Ostrovsky, L. A., & Stepanyants, Y. A. (2005). Internal solitons in laboratory experiments:
Comparison with theoretical models. Chaos, 28, 037111.
26. Pelinovsky, E. N., Rayevsky, M. A., & Shavratsky, S. K. (1977). The Korteweg-de Vries equation for nonstationary internal waves in an inhomogeneous ocean. Izvestiya, Atmospheric and
Oceanic Physics, 13, 226–228.
27. Vlasenko, V. I., Stashchuk, N. M., & Hutter, K. (2005). Baroclinic tides: Theoretical modelling
and observational evidence. Cambridge University Press.
28. Whitham, G. B. (1965). Nonlinear dispersive waves. Proceedings of the Royal Society of
London A, 283, 238–261.
29. Whitham, G. B. (1974). Linear and nonlinear waves. Wiley.
30. Zhou, X., & Grimshaw, R. (1989). The effect of variable currents on internal solitary waves.
Dynamics of Atmospheres and Oceans, 14, 17–39.
39
11. Grimshaw, R. (2010). Transcritical flow past an obstacle. ANZIAM Journal, 52, 1–25.
12. Grimshaw, R. (2015). Change of polarity for periodic waves in the variable-coefficient
Korteweg-de Vries equation. Studies in Applied Mathematics, 134, 363–371.
13. Grimshaw, R. H. J., & Smyth, N. F. (1986). Resonant flow of a stratified fluid over topography.
Journal of Fluid Mechanics, 169, 429–464.
14. Grimshaw, R., Pelinovsky, E., & Talipova, T. (2007). Modeling internal solitary waves in the
coastal ocean. Surveys in Geophysics, 28, 273–298.
15. Grimshaw, R., Pelinovsky, E., Talipova, T., & Kurkina, A. (2010). Internal solitary waves:
Propagation, deformation and disintegration. Nonlinear Processes in Geophysics, 17, 633–
649.
16. Grimshaw, R., & Yuan, C. (2016). The propagation of internal undular bores over variable
topography. Physica D, 333, 200–207.
17. Grimshaw, R., & Yuan, C. (2016). Depression and elevation tsunami waves in the framework
of the Korteweg-de Vries equation. Natural Hazards, 84, S493–S511.
18. Gurevich, A. V., & Pitaevskii, L. P. (1974). Nonstationary structure of a collisionless shock
wave. Soviet Physics JETP, 38, 291–297.
19. Helfrich, K. R., & Melville, W. K. (2006). Long nonlinear internal waves. Annual Review of
Fluid Mechanics, 38, 395–425.
20. Holloway, P., Pelinovsky, E., & Talipova, T. (2001). Internal tide transformation and oceanic
internal solitary waves. In R. Grimshaw (Ed.), Environmental stratified flows (pp. 31–60).
Boston: Kluwer.
21. Kamchatnov, A. M. (2000). Nonlinear periodic waves and their modulations. An introductory
course. World Scientific.
22. Kamchatnov, A. M. (2004). On Whitham theory for perturbed integrable equations. Physica
D, 188, 247–281.
23. Liu, Z., Grimshaw, R., & Johnson, E. (2017). Internal solitary waves propagating through variable background hydrology and currents. Ocean Modelling.
24. Myint, S., & Grimshaw, R. (1995). The modulation of nonlinear periodic wavetrains by dissipative terms in the Korteweg-de Vries equation. Wave Motion, 22, 215–238.
25. Ostrovsky, L. A., & Stepanyants, Y. A. (2005). Internal solitons in laboratory experiments:
Comparison with theoretical models. Chaos, 28, 037111.
26. Pelinovsky, E. N., Rayevsky, M. A., & Shavratsky, S. K. (1977). The Korteweg-de Vries equation for nonstationary internal waves in an inhomogeneous ocean. Izvestiya, Atmospheric and
Oceanic Physics, 13, 226–228.
27. Vlasenko, V. I., Stashchuk, N. M., & Hutter, K. (2005). Baroclinic tides: Theoretical modelling
and observational evidence. Cambridge University Press.
28. Whitham, G. B. (1965). Nonlinear dispersive waves. Proceedings of the Royal Society of
London A, 283, 238–261.
29. Whitham, G. B. (1974). Linear and nonlinear waves. Wiley.
30. Zhou, X., & Grimshaw, R. (1989). The effect of variable currents on internal solitary waves.
Dynamics of Atmospheres and Oceans, 14, 17–39.