Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 143
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Baronio, Fabio Wabnitz, Stefan and Kodama, Yuji 2016. Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin. Physical Review Letters, Vol. 116, Issue. 17,


    Chang, Jen-Hsu 2016. The interactions of solitons in the Novikov–Veselov equation. Applicable Analysis, Vol. 95, Issue. 6, p. 1370.


    Yuliawati, Lia Subasita, Nugrahinggil Adytia, Didit and Budhi, Wono Setya 2016. Vol. 1707, Issue. , p. 040003.

    Boruah, A. Sharma, S. K. Bailung, H. and Nakamura, Y. 2015. Oblique collision of dust acoustic solitons in a strongly coupled dusty plasma. Physics of Plasmas, Vol. 22, Issue. 9, p. 093706.


    Horowitz, Shai and Zarmi, Yair 2015. Kadomtsev–Petviashvili II equation: Structure of asymptotic soliton webs. Physica D: Nonlinear Phenomena, Vol. 300, p. 1.


    NAKAYAMA, Keisuke 2015. ANALYSIS OF SOLITON RESONANCE BY USING FULLY-NONLINEAR AND STRONGLY-DISPERSIVE WAVE MODEL. Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 71, Issue. 2, p. I_1.


    Velarde, Manuel G. and Vignes-Adler, Michele 2015. Encyclopedia of Surface and Colloid Science, Third Edition.


    Zha, Xiao Sun, He Xu, Tao Meng, Xiang-Hua and Li, Heng-Ji 2015. Soliton Interactions of the “Good” Boussinesq Equation on a Nonzero Background. Communications in Theoretical Physics, Vol. 64, Issue. 4, p. 367.


    Chakravarty, Sarbarish and Kodama, Yuji 2014. KP web-solitons from wave patterns: an inverse problem. Journal of Physics: Conference Series, Vol. 482, p. 012007.


    Chakravarty, Sarbarish and Kodama, Yuji 2014. Construction of KP solitons from wave patterns. Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue. 2, p. 025201.


    Kodaira, T. Waseda, T. and Miyazawa, Y. 2014. Nonlinear internal waves generated and trapped upstream of islands in the Kuroshio. Geophysical Research Letters, Vol. 41, Issue. 14, p. 5091.


    Kol, Guy Kingni, Sifeu and Woafo, Paul 2014. Rogue waves in Lugiato-Lefever equation with variable coefficients. Open Physics, Vol. 12, Issue. 11,


    Sakkaravarthi, K. Kanna, T. Vijayajayanthi, M. and Lakshmanan, M. 2014. Multicomponent long-wave–short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons. Physical Review E, Vol. 90, Issue. 5,


    Wang, Chuanjian and Dai, Zhengde 2014. Breather-type multi-solitary waves to the Kadomtsev–Petviashvili equation with positive dispersion. Applied Mathematics and Computation, Vol. 235, p. 332.


    Xue, Jingshuang Graber, Hans C. Romeiser, Roland and Lund, Bjorn 2014. Understanding Internal Wave–Wave Interaction Patterns Observed in Satellite Images of the Mid-Atlantic Bight. IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, Issue. 6, p. 3211.


    Yeh, Harry and Li, Wenwen 2014. Laboratory realization of KP-solitons. Journal of Physics: Conference Series, Vol. 482, p. 012046.


    YOSHIE, Yuto and NAKAYAMA, Keisuke 2014. Numerical Simulation of Solitary Waves using a Fully-nonlinear Strongly-dispersive Wave Equation with Vorticity. Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), Vol. 70, Issue. 2, p. I_1.


    Zarmi, Yair 2014. Vertex dynamics in multi-soliton solutions of Kadomtsev–Petviashvili II equation. Nonlinearity, Vol. 27, Issue. 6, p. 1499.


    Ablowitz, M. J. and Curtis, C. W. 2013. Conservation laws and non-decaying solutions for the Benney-Luke equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 469, Issue. 2152, p. 20120690.


    Khusnutdinova, K. R. Klein, C. Matveev, V. B. and Smirnov, A. O. 2013. On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 23, Issue. 1, p. 013126.


    ×

Resonantly interacting solitary waves

  • John W. Miles (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112077000093
  • Published online: 01 April 2006
Abstract

Resonant (phase-locked) interactions among three obliquely oriented solitary waves are studied. It is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves. The latter include regular reflexion at a rigid wall, which is impossible for ϕi < (3α)½ (ϕ = angle of incidence, α = amplitude/depth [Lt ] 1), and it is shown that the observed phenomenon of ‘Mach reflexion’ can be described as a resonant interaction in this regime. The run-up at the wall is calculated as a function of ϕi/(3α)½ and is found to have a maximum value of 4αd for ϕi = (3α)½. This same resonant interaction also describes diffraction of a solitary wave at a corner of internal angle π − ψi, −(3α)½, and suggests that a solitary wave cannot turn through an angle in excess of (3α)½ at a convex corner without separating or otherwise losing its identity.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax