Summary.
The Bäcklund-Darboux transformations are successfully utilized to construct heteroclinic orbits of Davey-Stewartson II equations through an elegant iteration of the transformations. In [17], we successfully built Melnikov vectors with the gradients of Floquet discriminants. Since there is no Floquet discriminant for Davey-Stewartson equations (in contrast to nonlinear Schrödinger equations [17]), the Melnikov vectors here are built with the novel idea of replacing the gradients of Floquet discriminants by quadratic products of Bloch functions. Such Melnikov vectors still maintain the properties of Poisson commuting with the gradient of the Hamiltonian and exponential decay as time approaches positive and negative infinities. This solves the problem of building Melnikov vectors for Davey-Stewartson equations without using the gradients of a Floquet discriminant. Melnikov functions for perturbed Davey-Stewartson II equations evaluated on the above heteroclinic orbits are built.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Original received on June 2, 1998; revised manuscript accepted for publication on June 18, 1999
Rights and permissions
About this article
Cite this article
Li, Y. B{ä}cklund-Darboux Transformations and Melnikov Analysis for Davey-Stewartson II Equations. J. Nonlinear Sci. 10, 103–131 (2000). https://doi.org/10.1007/s003329910005
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003329910005