Title:

  The dual-Petrov-Galerkin method for the solitary waves with or without
damped oscillatory tails in the fifth-order Korteweg-de Vries equation


Abstract:

The fifth-order KdV-type equation models many physical phenomena such as
gravity-capillary waves and magneto-sound propagation in 
plasma.Dual-Petrov-Galerkin approximations to the fifth-order KdV equation 
is considered. The key idea of this method developed by Jie Shen is to use 
the trial functions satisfying the underlying boundary conditions of the 
differential equation and the test functions satisfying the dual boundary
conditions. Our theoretical analysis and numerical results indicate the 
proposed dual-Petrov-Galerkin method is extremely accurate and efficient. 
This is a joint work with Jie Shen and Jiahong Wu.