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On a new 3D generalized Hunter-Saxton equation

Sergei Sakovich

Abstract

The problem of integrability is studied for a 3D generalized Hunter-Saxton equation introduced recently by O.I. Morozov. A transformation is found which brings the equation into a constant-characteristic form and simultaneously trivializes the equation's Lax representation. The transformed equation is shown to fail the Painleve test for integrability.

On a new 3D generalized Hunter-Saxton equation

Abstract

The problem of integrability is studied for a 3D generalized Hunter-Saxton equation introduced recently by O.I. Morozov. A transformation is found which brings the equation into a constant-characteristic form and simultaneously trivializes the equation's Lax representation. The transformed equation is shown to fail the Painleve test for integrability.
Paper Structure (4 sections, 25 equations)

This paper contains 4 sections, 25 equations.

Table of Contents

  1. Introduction
  2. Transformation
  3. Singularity analysis
  4. Conclusion