Fourth-order coupled nonlinear Schrodinger equations for gravity waves on deep water

被引：30
|
作者：
Gramstad, Odin [1 ]
Trulsen, Karsten [1 ]
机构：
[1] Univ Oslo, Dept Math, NO-0316 Oslo, Norway
来源：
PHYSICS OF FLUIDS | 2011年 / 23卷 / 06期
关键词：
flow instability; gravity waves; nonlinear differential equations; Schrodinger equation; water waves; EVOLUTION EQUATION; FINITE GEOMETRIES; SURFACE-WAVES; FREAK WAVES; SPECTRA; SEA;
D O I：
10.1063/1.3598316
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
We derive a set of two fourth-order coupled nonlinear Schrodinger equations describing the evolution of two two-dimensional systems of deep-water gravity waves with different wavenumbers or directions of propagation. It is shown that the coupled equations can be formulated as a Hamiltonian system and that they conserve the total wave action and momentum of the combined wave field. The modulational instability of two interacting uniform wave trains is considered. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598316]
引用
收藏
页数：9
相关论文
共 50 条
  • [41] The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
    Osborne, AR
    Onorato, M
    Serio, M
    PHYSICS LETTERS A, 2000, 275 (5-6) : 386 - 393
  • [42] Modelling of the temporal and spatial evolutions of weakly nonlinear random directional waves with the modified nonlinear Schrodinger equations
    Zhang, H. D.
    Guedes Soares, C.
    Onorato, M.
    Toffoli, A.
    APPLIED OCEAN RESEARCH, 2016, 55 : 130 - 140
  • [43] NORMALIZED SOLUTIONS FOR 3-COUPLED NONLINEAR SCHRODINGER EQUATIONS
    Liu, Chuangye
    Tian, Rushun
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (11) : 5115 - 5130
  • [44] Existence of solutions for fourth-order ODE's in water wave models
    Aprahamian, M. O.
    Tersian, S. A.
    MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE, 2009, 1124 : 39 - +
  • [45] Scattering of solutions with group invariance for the fourth-order nonlinear Schrödinger equation
    Komada, Koichi
    Masaki, Satoshi
    NONLINEARITY, 2024, 37 (08)
  • [46] Stability of bichromatic gravity waves on deep water
    Leblanc, Stephane
    EUROPEAN JOURNAL OF MECHANICS B-FLUIDS, 2009, 28 (05) : 605 - 612
  • [47] On the kurtosis of deep-water gravity waves
    Fedele, Francesco
    JOURNAL OF FLUID MECHANICS, 2015, 782 : 25 - 36
  • [48] Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p-Laplacian-like Operators and Neutral Delay Arguments
    Alatwi, Mansour
    Moaaz, Osama
    Albalawi, Wedad
    Masood, Fahd
    El-Metwally, Hamdy
    MATHEMATICS, 2024, 12 (03)
  • [49] On asymptotic stability of solitary waves in Schrodinger equation coupled to nonlinear oscillator
    Buslaev, V. S.
    Komech, A. I.
    Kopylova, E. A.
    Stuart, D.
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (04) : 669 - 705
  • [50] Linear-shear-current modified nonlinear Schrödinger equation for gravity-capillary waves on deep water
    Pal, Tanmoy
    Dhar, Asoke Kumar
    MECCANICA, 2024, 59 (05) : 743 - 759
12345