On a new 3D generalized Hunter-Saxton equation
Sergei Sakovich
TL;DR
This paper investigates the integrability of a new 3D generalized Hunter-Saxton equation, finding a transformation that simplifies the equation but reveals it is not integrable via the Painleve test.
Contribution
It introduces a transformation that simplifies the 3D generalized Hunter-Saxton equation and analyzes its integrability properties.
Findings
Transformation simplifies the equation to constant-characteristic form
The equation's Lax representation is trivialized by the transformation
The equation fails the Painleve test for integrability
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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Fractional Differential Equations Solutions · Advanced Fiber Optic Sensors