On the Construction of a Modulating Multiphase Wavetrain for a Perturbed KdV Equation.
NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES
Pagination or Media Count:
This paper summarizes the status of a direct construction of an asymptotic representation of a modulating multiphase wavetrain for a class of perturbed KdV equations. This class includes the KdV-Burgers equation. The calculations apply on a boundary between dispersive and dissipative behavior. The construction proceeds by standard asymptotic methods. The result of the construction is an invariant representation of the reduced equations which permits their diagonalization. While mathematically the construction is incomplete, care is taken to correctly identify the mathematical status of each step in the construction. The equivalence of this constructive approach with the postulated averaging of conversation laws is established for two phase waves. Author
- Theoretical Mathematics