DocumentCode
2323489
Title
Symmetries and exact solutions to a nonlinear doubly dispersive equation with dissipation
Author
Gursky, Vitaly V. ; Samsonov, Alexander M.
Author_Institution
A.F. Ioffe Physicotech. Inst., Acad. of Sci., St. Petersburg, Russia
fYear
2001
fDate
2001
Firstpage
107
Lastpage
115
Abstract
Nonclassical Lie symmetries of a nonlinear doubly dispersive and dissipative equation are studied. The equation appears in modelling the nonlinear longitudinal density wave propagation in an elastic rod embedded into an external dissipative medium. Using the symmetries, new exact invariant solutions are found. The comparison of the nonclassical symmetry method with various ad hoc methods of finding exact solutions is considered
Keywords
absorbing media; cooling; heat conduction; nonlinear equations; wave propagation; dissipation; dissipative medium; elastic rod; exact invariant solutions; exact solutions; nonclassical Lie symmetries; nonclassical symmetry method; nonlinear doubly dispersive equation; nonlinear doubly dissipative equation; nonlinear heat conduction equation; nonlinear longitudinal density wave propagation; travelling wave solutions; Boundary conditions; Capacitive sensors; Diffraction; Dispersion; Nonlinear equations; Surface waves; Viscosity;
fLanguage
English
Publisher
ieee
Conference_Titel
Day on Diffraction 2001. Proceedings. International Seminar
Conference_Location
St.Petersburg
Print_ISBN
5-7997-0366-9
Type
conf
DOI
10.1109/DD.2001.988463
Filename
988463
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