Huygens' principle for hyperbolic operators and integrable hierarchies

Fabio A.C.C. Chalub, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We show that the stationary solutions of the canonical AKNS hierarchy of nonlinear evolution equations yield perturbations of Dirac operators that satisfy a strict form of Huygens' principle. Namely, the domain of dependence of such Dirac operators at any given point y is contained in the light-cone's hypersurface issued from y. By the canonical AKNS hierarchy we mean that the differential polynomials defining the flows are isobaric with respect to certain weights. The method we employ is of interest by itself. Indeed, we consider the Riesz kernels associated to a given hyperbolic differential operator and expand the fundamental solution of perturbations of this operator in a series in such Riesz kernels. Using the coefficients of this Hadamard type expansion we introduce a family of vector fields. For the D'Alembertian such vector field family corresponds to the KdV hierarchy and for the Dirac operators they include the AKNS one.

Original languageBritish English
Pages (from-to)231-245
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Issue number2
StatePublished - 15 Jan 2006


  • Dirac operators
  • Huygens' principle
  • Rational solutions of integrable equations


Dive into the research topics of 'Huygens' principle for hyperbolic operators and integrable hierarchies'. Together they form a unique fingerprint.

Cite this