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The nonlinear Schrödinger equation created by the vibrations of an elastic plate and its dimensional expansion

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  • We first survey the two-dimensional governing equation that describes the propagation of a wave packet on an elastic plate using the method of multiple scales by [13]. We next expand the governing equation to the multi-dimensional case not only in the sense of mathematical science but also engineering.
    Mathematics Subject Classification: Primary: 35L05; Secondary: 35Q55.

    Citation:

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  • [1]

    G. P. Agrawal, "Fiber-Optic Communication System," 2nd editon, Wiley, New York, 1997.

    [2]

    R. C. Averill and J. N. Reddy, Behavior of plate elements based on the first-order shear deformation theory, Engineering Computations, 7 (1990), 57-74.

    [3]

    S. K. Chakrabarti, R. H. Snider and P. H. Feldhausen, Mean length of runs of ocean waves, Journal of Geophysical Research, 79(1974), 5665-5667.

    [4]

    H. N. Chu and G. Herrmann, Influence of large amplitudes on free flexural vibrations of rectangular elastic plates, Journal of Applied Mechnics, 23 (1956), 532-540.

    [5]

    Y. Goda, Numerical experiments on wave statistics with spectral simulation, Report Port Harbour Research Institute, 9 (1970), 3-57.

    [6]

    R. Haberman, "Elementary Applied Partial Differential Equations," Prentice Hall, Englewood Cliff, NJ, 1983.

    [7]

    M .M. Hrabok and T. M. Hrudey, A review and catalog of plate bending finite elements, Computers and Structures, 19 (1984), 479-495.

    [8]

    S. Kanagawa, K. Tchizawa and T. Nitta, Solutions of Ginzburg-Landau Equations Induced from Multi-dimensional Bichromatic Waves and Some Examples of Their Envelope Functions, Theoretical and Applied Mechanics Japan, 58 (2009), 71-78.

    [9]

    S. Kanagawa, K. Tchizawa and T. Nitta, Ginzburg-Landau equations induced from multi-dimensional bichromatic waves, Nonlinear Analysis: Theory, Methods & Applications, 71 (2009), e2258-e2266.

    [10]

    S. Kanagawa, T. Nitta and K. Tchizawa, Approximated Solutions of Schrodinger Equations Induced from Nearly Monochromatic Waves, Theoretical and Applied Mechanics Japan, 59 (2010), 153-161.

    [11]

    A. W. Leissa, "Vibration of Plates," NASA-Sp-160, 1969.

    [12]

    M. S. Longuet-Higgins, Statistical properties of wave groups in a random sea-state, Philosophical Transactions of the Royal Society of London, Series A, 312(1984), 219-250.

    [13]

    A. H. Nayfeh, "Perturbation Methods," Wiley, New York, 2002.

    [14]

    B. T. Nohara, Governing Equations of Envelope Surface Created by Directional, Nearly Monochromatic Waves, Journal of Society of Industrial and Applied Mathematics, 13 (2003), 75-86. (in Japanese)

    [15]

    B. T. Nohara, Derivation and consideration of governing equations of the envelope surface created by directional, nearly monochromatic waves, International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, 31 (2003), 375-392.

    [16]

    B. T. Nohara, Governing Equations of Envelope Surface Created by Nearly Bichromatic Waves Propagating on an Elastic Plate and Their Stability, Japan Journal of Industrial and Applied Mathematics, 22 (2005), 87-109.

    [17]

    B. T. Nohara and A. Arimoto, The stability of the governing equation of envelope surface created by nearly bichromatic waves propagating on an elastic plate, Nonlinear Analysis: Theory, Methods & Applications, 63 (2005), e2197-e2208.

    [18]

    B. T. Nohara and A. Arimoto, On the Quintic Nonlinear Schrodinger Equation Created by the Vibrations of a Square Plate on a Weakly Nonlinear Elastic Foundation and the Stability of the Uniform Solution, Japan Journal of Industrial and Applied Mathematics, 24 (2007), 161-179.

    [19]

    B. T. Nohara and A. Arimoto and T. Saigo, Governing Equations of Envelopes Created by Nearly Bichromatic Waves and Relation to the Nonlinear Schrödinger Equation, Chaos, Solitons and Fractals, 35 (2008), 942-948.

    [20]

    J. N. Reddy, "An Introduction to the Finite Element Method," 2nd edition., McGraw-Hill, New York, 1993.

    [21]

    H. Reismann, "Elastic Plates: Theory and Application," Wiley, New Jersey, 1988.

    [22]

    S. P. Timoshenko, "Theory of Plates and Shells," McGraw-Hill, New York, 1940.

    [23]

    S. P. Timoshenko and S. Woinowsky-Krieger, "Theory of Plates and Shells," McGraw-Hill, Singapore, 1970.

    [24]

    A. C. Ugural, "Stresses in plates and shells," McGraw-Hill, New York, 1981.

    [25]

    H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude, Physics Review Letters, 17 (1966), 996-998.

    [26]

    M.A. Zarubinskaya and W.T. van Horssen, On the Vibration on a Simply Supported Square Plate on a Weakly Nonlinear Elastic Fooundation, International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, 40 (2005), 35-60.

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