Evolution equations,singular dispersion relations,and moving eigenvalues |
| |
Authors: | David J Kaup Alan C Newell |
| |
Institution: | Department of Physics, Clarkson College of Technology, Potsdam, New York 13676 USA;Department of Mathematics, Clarkson College of Technology, Potsdam, New York 13676 USA |
| |
Abstract: | A new approach for finding the class of integrable evolution equations associated with a given eigenvalue problem is developed. The key point to note is that the squares of the eigenfunctions form a natural basis in which to expand the solutions of the evolution equation. Once this step is taken, the class of integrable equations may usually be read off by inspection. Of particular interest are those equations for which the bound state eigenvalues are not invariant but move in a way prescribed by the coefficients of the evolution equation. The corresponding solitons have the property that they retain their identity on collision with other solution components, but this identity is no longer a constant one. The Hamiltonian structure and the causality properties of these systems are also explored. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|