Evolution equations, singular dispersion relations, and moving eigenvalues

David J. Kaup, Alan C. Newell

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)67-100
Number of pages34
JournalAdvances in Mathematics
Issue number1
StatePublished - Jan 1979

ASJC Scopus subject areas

  • General Mathematics


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