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The nonlinear Schrödinger equation created by the vibrations of an elastic plate and its dimensional expansion
1. | Department of Mathematics, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan |
2. | Department of Information Science, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan |
References:
[1] |
G. P. Agrawal, "Fiber-Optic Communication System,", 2nd editon, (1997). Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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.
|
[5] |
Y. Goda, Numerical experiments on wave statistics with spectral simulation,, Report Port Harbour Research Institute, 9 (1970), 3. Google Scholar |
[6] |
R. Haberman, "Elementary Applied Partial Differential Equations,", Prentice Hall, (1983).
|
[7] |
M .M. Hrabok and T. M. Hrudey, A review and catalog of plate bending finite elements,, Computers and Structures, 19 (1984), 479. Google Scholar |
[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.
|
[9] |
S. Kanagawa, K. Tchizawa and T. Nitta, Ginzburg-Landau equations induced from multi-dimensional bichromatic waves,, Nonlinear Analysis: Theory, 71 (2009).
|
[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. Google Scholar |
[11] |
A. W. Leissa, "Vibration of Plates,", NASA-Sp-160, (1969). Google Scholar |
[12] |
M. S. Longuet-Higgins, Statistical properties of wave groups in a random sea-state,, Philosophical Transactions of the Royal Society of London, 312 (1984), 219.
|
[13] |
A. H. Nayfeh, "Perturbation Methods,", Wiley, (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.
|
[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.
|
[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.
|
[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, 63 (2005). Google Scholar |
[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.
|
[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, 35 (2008), 942.
|
[20] |
J. N. Reddy, "An Introduction to the Finite Element Method," 2nd edition.,, McGraw-Hill, (1993). Google Scholar |
[21] |
H. Reismann, "Elastic Plates: Theory and Application,", Wiley, (1988). Google Scholar |
[22] |
S. P. Timoshenko, "Theory of Plates and Shells,", McGraw-Hill, (1940). Google Scholar |
[23] |
S. P. Timoshenko and S. Woinowsky-Krieger, "Theory of Plates and Shells,", McGraw-Hill, (1970). Google Scholar |
[24] |
A. C. Ugural, "Stresses in plates and shells,", McGraw-Hill, (1981). Google Scholar |
[25] |
H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude,, Physics Review Letters, 17 (1966), 996. Google Scholar |
[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.
|
show all references
References:
[1] |
G. P. Agrawal, "Fiber-Optic Communication System,", 2nd editon, (1997). Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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.
|
[5] |
Y. Goda, Numerical experiments on wave statistics with spectral simulation,, Report Port Harbour Research Institute, 9 (1970), 3. Google Scholar |
[6] |
R. Haberman, "Elementary Applied Partial Differential Equations,", Prentice Hall, (1983).
|
[7] |
M .M. Hrabok and T. M. Hrudey, A review and catalog of plate bending finite elements,, Computers and Structures, 19 (1984), 479. Google Scholar |
[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.
|
[9] |
S. Kanagawa, K. Tchizawa and T. Nitta, Ginzburg-Landau equations induced from multi-dimensional bichromatic waves,, Nonlinear Analysis: Theory, 71 (2009).
|
[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. Google Scholar |
[11] |
A. W. Leissa, "Vibration of Plates,", NASA-Sp-160, (1969). Google Scholar |
[12] |
M. S. Longuet-Higgins, Statistical properties of wave groups in a random sea-state,, Philosophical Transactions of the Royal Society of London, 312 (1984), 219.
|
[13] |
A. H. Nayfeh, "Perturbation Methods,", Wiley, (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.
|
[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.
|
[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.
|
[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, 63 (2005). Google Scholar |
[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.
|
[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, 35 (2008), 942.
|
[20] |
J. N. Reddy, "An Introduction to the Finite Element Method," 2nd edition.,, McGraw-Hill, (1993). Google Scholar |
[21] |
H. Reismann, "Elastic Plates: Theory and Application,", Wiley, (1988). Google Scholar |
[22] |
S. P. Timoshenko, "Theory of Plates and Shells,", McGraw-Hill, (1940). Google Scholar |
[23] |
S. P. Timoshenko and S. Woinowsky-Krieger, "Theory of Plates and Shells,", McGraw-Hill, (1970). Google Scholar |
[24] |
A. C. Ugural, "Stresses in plates and shells,", McGraw-Hill, (1981). Google Scholar |
[25] |
H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude,, Physics Review Letters, 17 (1966), 996. Google Scholar |
[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.
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