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Volumn 2014, Issue , 2014, Pages

Modelling fractal waves on shallow water surfaces via local fractional korteweg-de vries equation

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EID: 84903541046     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2014/278672     Document Type: Article
Times cited : (69)

References (30)
  • 1
    • 84903548678 scopus 로고
    • Imprimerie Nationale Mémoires Présentés par Divers Savants à l'Académie des Sciences de l'Institut National de France
    • Boussinesq J., Essai sur la Théorie des Eaux Courantes 1877 23 Imprimerie Nationale Mémoires Présentés par Divers Savants à l'Académie des Sciences de l'Institut National de France
    • (1877) Essai sur la Théorie des Eaux Courantes , vol.23
    • Boussinesq, J.1
  • 2
    • 0001524186 scopus 로고
    • XLI. on the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • 10.1080/14786449508620739
    • Korteweg D. J., de Vries G., XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 1895 39 240 422 443 10.1080/14786449508620739
    • (1895) The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , vol.39 , Issue.240 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 3
    • 49449124267 scopus 로고
    • The Korteweg-de vries-burgers equation
    • 2-s2.0-49449124267
    • Canosa J., Gazdag J., The Korteweg-de Vries-Burgers equation. Journal of Computational Physics 1977 23 4 393 403 2-s2.0-49449124267
    • (1977) Journal of Computational Physics , vol.23 , Issue.4 , pp. 393-403
    • Canosa, J.1    Gazdag, J.2
  • 4
    • 0000788656 scopus 로고
    • Solitons from sine waves: Analytical and numerical methods for non-integrable solitary and cnoidal waves
    • 2-s2.0-0000788656
    • Boyd J. P., Solitons from sine waves: analytical and numerical methods for non-integrable solitary and cnoidal waves. Physica D: Nonlinear Phenomena 1986 21 2-3 227 246 2-s2.0-0000788656
    • (1986) Physica D: Nonlinear Phenomena , vol.21 , Issue.2-3 , pp. 227-246
    • Boyd, J.P.1
  • 5
    • 78751507852 scopus 로고
    • On the generalized Korteweg-de Vries equation
    • 10.3792/pja/1195520159
    • Tsutsumi M., Mukasa T., Iino R., On the generalized Korteweg-de Vries equation. Proceedings of the Japan Academy 1970 46 9 921 925 10.3792/pja/1195520159
    • (1970) Proceedings of the Japan Academy , vol.46 , Issue.9 , pp. 921-925
    • Tsutsumi, M.1    Mukasa, T.2    Iino, R.3
  • 8
    • 0004531797 scopus 로고
    • On the inverse scattering transform, the cylindrical Korteweg-de Vries equation and similarity solutions
    • 2-s2.0-0004531797
    • Johnson R. S., On the inverse scattering transform, the cylindrical Korteweg-de Vries equation and similarity solutions. Physics Letters A 1979 72 3 197 199 2-s2.0-0004531797
    • (1979) Physics Letters A , vol.72 , Issue.3 , pp. 197-199
    • Johnson, R.S.1
  • 9
    • 0001120168 scopus 로고
    • The geometry of the KdV equation
    • 10.1142/S0217751X91001416
    • Segal G., The geometry of the KdV equation. International Journal of Modern Physics A 1991 6 16 2859 2869 10.1142/S0217751X91001416
    • (1991) International Journal of Modern Physics A , vol.6 , Issue.16 , pp. 2859-2869
    • Segal, G.1
  • 10
    • 0001526429 scopus 로고
    • Stochastic Korteweg-de Vries equation
    • 2-s2.0-0001526429
    • Wadati M., Stochastic Korteweg-de Vries equation. Journal of the Physical Society of Japan 1983 52 8 2642 2648 2-s2.0-0001526429
    • (1983) Journal of the Physical Society of Japan , vol.52 , Issue.8 , pp. 2642-2648
    • Wadati, M.1
  • 11
    • 36849110505 scopus 로고
    • Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation
    • 2-s2.0-36849110505 10.1063/1.1664700
    • Miura R. M., Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation. Journal of Mathematical Physics 1968 9 8 1202 1204 2-s2.0-36849110505 10.1063/1.1664700
    • (1968) Journal of Mathematical Physics , vol.9 , Issue.8 , pp. 1202-1204
    • Miura, R.M.1
  • 12
    • 0019559935 scopus 로고
    • The Korteweg-de Vries equation: A historical essay
    • 2-s2.0-0019559935
    • Miles J. W., The Korteweg-de Vries equation: a historical essay. Journal of Fluid Mechanics 1981 106 131 147 2-s2.0-0019559935
    • (1981) Journal of Fluid Mechanics , vol.106 , pp. 131-147
    • Miles, J.W.1
  • 13
    • 38049162125 scopus 로고    scopus 로고
    • Variational iteration method for solving the space- and time-fractional KdV equation
    • 2-s2.0-38049162125 10.1002/num.20247
    • Momani S., Odibat Z., Alawneh A., Variational iteration method for solving the space- and time-fractional KdV equation. Numerical Methods for Partial Differential Equations 2008 24 1 262 271 2-s2.0-38049162125 10.1002/num.20247
    • (2008) Numerical Methods for Partial Differential Equations , vol.24 , Issue.1 , pp. 262-271
    • Momani, S.1    Odibat, Z.2    Alawneh, A.3
  • 14
    • 79959502347 scopus 로고    scopus 로고
    • Time-fractional KdV equation: Formulation and solution using variational methods
    • 2-s2.0-79959502347 10.1007/s11071-010-9873-5
    • El-Wakil S. A., Abulwafa E., Zahran M., Mahmoud A., Time-fractional KdV equation: formulation and solution using variational methods. Nonlinear Dynamics 2011 65 1-2 55 63 2-s2.0-79959502347 10.1007/s11071-010-9873-5
    • (2011) Nonlinear Dynamics , vol.65 , Issue.1-2 , pp. 55-63
    • El-Wakil, S.A.1    Abulwafa, E.2    Zahran, M.3    Mahmoud, A.4
  • 15
    • 84876534192 scopus 로고    scopus 로고
    • The time-fractional coupled-Korteweg-de-Vries equations
    • 2-s2.0-84876534192 10.1155/2013/947986 947986
    • Atangana A., Secer A., The time-fractional coupled-Korteweg-de-Vries equations. Abstract and Applied Analysis 2013 2013 8 2-s2.0-84876534192 10.1155/2013/947986 947986
    • (2013) Abstract and Applied Analysis , vol.2013 , pp. 8
    • Atangana, A.1    Secer, A.2
  • 16
    • 55549103342 scopus 로고    scopus 로고
    • Approximate analytical solution to fractional modified KdV equations
    • 2-s2.0-55549103342 10.1016/j.mcm.2008.01.005
    • Abdulaziz O., Hashim I., Ismail E. S., Approximate analytical solution to fractional modified KdV equations. Mathematical and Computer Modelling 2009 49 1-2 136 145 2-s2.0-55549103342 10.1016/j.mcm.2008.01.005
    • (2009) Mathematical and Computer Modelling , vol.49 , Issue.1-2 , pp. 136-145
    • Abdulaziz, O.1    Hashim, I.2    Ismail, E.S.3
  • 18
    • 84890267857 scopus 로고    scopus 로고
    • Transport equations in fractal porous media within fractional complex transform method
    • Yang X.-J., Baleanu D., He J.-H., Transport equations in fractal porous media within fractional complex transform method. Proceedings of the Romanian Academy A 2013 14 4 287 292
    • (2013) Proceedings of the Romanian Academy A , vol.14 , Issue.4 , pp. 287-292
    • Yang, X.-J.1    Baleanu, D.2    He, J.-H.3
  • 19
    • 84881521586 scopus 로고    scopus 로고
    • Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates
    • 2-s2.0-84881521586 10.1155/2013/754248 754248
    • Hao Y.-J., Srivastava H. M., Jafari H., Yang X.-J., Helmholtz and diffusion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates. Advances in Mathematical Physics 2013 2013 5 2-s2.0-84881521586 10.1155/2013/754248 754248
    • (2013) Advances in Mathematical Physics , vol.2013 , pp. 5
    • Hao, Y.-J.1    Srivastava, H.M.2    Jafari, H.3    Yang, X.-J.4
  • 21
    • 84880084367 scopus 로고    scopus 로고
    • Systems of Navier-Stokes equations on cantor sets
    • 2-s2.0-84880084367 10.1155/2013/769724 769724
    • Yang X.-J., Baleanu D., Tenreiro Machado J. A., Systems of Navier-Stokes equations on cantor sets. Mathematical Problems in Engineering 2013 2013 8 2-s2.0-84880084367 10.1155/2013/769724 769724
    • (2013) Mathematical Problems in Engineering , vol.2013 , pp. 8
    • Yang, X.-J.1    Baleanu, D.2    Tenreiro Machado, J.A.3
  • 22
    • 84897825779 scopus 로고    scopus 로고
    • Local fractional Fourier series solutions for non-homogeneous heat equations arising in fractal heat flow with local fractional derivative
    • 514639 10.1155/2014/514639
    • Yang A. M., Cattani C., Zhang C., Xie G. N., Yang X. J., Local fractional Fourier series solutions for non-homogeneous heat equations arising in fractal heat flow with local fractional derivative. Advances in Mechanical Engineering 2014 2014 5 514639 10.1155/2014/514639
    • (2014) Advances in Mechanical Engineering , vol.2014 , pp. 5
    • Yang, A.M.1    Cattani, C.2    Zhang, C.3    Xie, G.N.4    Yang, X.J.5
  • 23
    • 84900011952 scopus 로고    scopus 로고
    • Local fractional Poisson and Laplace equations with applications to electrostatics in fractal domain
    • 590574 10.1155/2014/590574
    • Li Y. Y., Zhao Y., Xie G. N., Baleanu D., Yang X. J., Zhao K., Local fractional Poisson and Laplace equations with applications to electrostatics in fractal domain. Advances in Mathematical Physics 2014 2014 5 590574 10.1155/2014/590574
    • (2014) Advances in Mathematical Physics , vol.2014 , pp. 5
    • Li, Y.Y.1    Zhao, Y.2    Xie, G.N.3    Baleanu, D.4    Yang, X.J.5    Zhao, K.6
  • 24
    • 84897565366 scopus 로고    scopus 로고
    • Mathematical models arising in the fractal forest gap via local fractional calculus
    • 782393 10.1155/2014/782393
    • Long C. Y., Zhao Y., Jafari H., Mathematical models arising in the fractal forest gap via local fractional calculus. Abstract and Applied Analysis 2014 2014 6 782393 10.1155/2014/782393
    • (2014) Abstract and Applied Analysis , vol.2014 , pp. 6
    • Long, C.Y.1    Zhao, Y.2    Jafari, H.3
  • 25
    • 84893184829 scopus 로고    scopus 로고
    • Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative
    • 176395 10.1155/2014/176395
    • Wang S. Q., Yang Y. J., Jassim H. K., Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative. Abstract and Applied Analysis 2014 2014 7 176395 10.1155/2014/176395
    • (2014) Abstract and Applied Analysis , vol.2014 , pp. 7
    • Wang, S.Q.1    Yang, Y.J.2    Jassim, H.K.3
  • 26
    • 84878016367 scopus 로고    scopus 로고
    • Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives
    • 2-s2.0-84878016367 10.1016/j.physleta.2013.04.012
    • Yang X.-J., Srivastava H. M., He J.-H., Baleanu D., Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives. Physics Letters A 2013 377 28-30 1696 1700 2-s2.0-84878016367 10.1016/j.physleta.2013.04.012
    • (2013) Physics Letters A , vol.377 , Issue.28-30 , pp. 1696-1700
    • Yang, X.-J.1    Srivastava, H.M.2    He, J.-H.3    Baleanu, D.4
  • 28
    • 84880863273 scopus 로고    scopus 로고
    • A new Neumann series method for solving a family of local fractional Fredholm and Volterra integral equations
    • 2-s2.0-84880863273 10.1155/2013/325121 325121
    • Ma X.-J., Srivastava H. M., Baleanu D., Yang X.-J., A new Neumann series method for solving a family of local fractional Fredholm and Volterra integral equations. Mathematical Problems in Engineering 2013 2013 6 2-s2.0-84880863273 10.1155/2013/325121 325121
    • (2013) Mathematical Problems in Engineering , vol.2013 , pp. 6
    • Ma, X.-J.1    Srivastava, H.M.2    Baleanu, D.3    Yang, X.-J.4
  • 29
    • 84890038237 scopus 로고    scopus 로고
    • Application of the local fractional series expansion method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators
    • 259125 10.1155/2013/259125
    • Yang A.-M., Chen Z.-S., Srivastava H. M., Yang X.-J., Application of the local fractional series expansion method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators. Abstract and Applied Analysis 2013 2013 6 259125 10.1155/2013/259125
    • (2013) Abstract and Applied Analysis , vol.2013 , pp. 6
    • Yang, A.-M.1    Chen, Z.-S.2    Srivastava, H.M.3    Yang, X.-J.4
  • 30
    • 84934914868 scopus 로고    scopus 로고
    • A local fractional integral inequality on fractal space analogous to Aderson's inequality
    • 797561 10.1155/2014/797561
    • Wei W., Srivastava H. M., Wang L., Shen P.-Y., Zhang J., A local fractional integral inequality on fractal space analogous to Aderson's inequality. Abstract and Applied Analysis 2014 2014 7 797561 10.1155/2014/797561
    • (2014) Abstract and Applied Analysis , vol.2014 , pp. 7
    • Wei, W.1    Srivastava, H.M.2    Wang, L.3    Shen, P.-Y.4    Zhang, J.5


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