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
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;
Conference_Titel :
Day on Diffraction 2001. Proceedings. International Seminar
Conference_Location :
St.Petersburg
Print_ISBN :
5-7997-0366-9
DOI :
10.1109/DD.2001.988463
