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Solitary Wave Formation from a Generalized Rosenau Equation
Joint Authors
Ramos, J. I.
García-López, C. M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-01-06
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
A generalized viscous Rosenau equation containing linear and nonlinear advective terms and mixed third- and fifth-order derivatives is studied numerically by means of an implicit second-order accurate method in time that treats the first-, second-, and fourth-order spatial derivatives as unknown and discretizes them by means of three-point, fourth-order accurate, compact finite differences.
It is shown that the effect of the viscosity is to decrease the amplitude, curve the wave trajectory, and increase the number and width of the waves that emerge from an initial Gaussian condition, whereas the linear convective term pushes the wave front towards the downstream boundary.
It is also shown that the effect of the nonlinear convective term is to increase the steepness of the leading wave front and the number of sawtooth waves that are generated behind it, while that of the first dispersive term is to increase the number of waves that break up from the initial condition as the coefficient that characterizes this term is decreased.
It is also shown that, for reasons of stability, the second dispersion coefficient must be much smaller than the first one and its effects on wave propagation are relatively small.
American Psychological Association (APA)
Ramos, J. I.& García-López, C. M.. 2016. Solitary Wave Formation from a Generalized Rosenau Equation. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1112207
Modern Language Association (MLA)
Ramos, J. I.& García-López, C. M.. Solitary Wave Formation from a Generalized Rosenau Equation. Mathematical Problems in Engineering No. 2016 (2016), pp.1-17.
https://search.emarefa.net/detail/BIM-1112207
American Medical Association (AMA)
Ramos, J. I.& García-López, C. M.. Solitary Wave Formation from a Generalized Rosenau Equation. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1112207
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112207