Work

Exact Solution of the Time-fractional Generalized Hunter–Saxton Model

Year: 2026

Type: article

Abstract: The Hunter–Saxton (HS) equation models the orientation dynamics of nematic liquid crystals and arises naturally in geometric hydrodynamics. Fractional generalizations of HS have become increasingly important due to their ability to incorporate memory effects and nonlocal temporal interactions. In this manuscript, we study a generalized HS-type model with a Caputo fractional derivative and variable nonlinear coefficients. We derive an exact analytic solution under a specific algebraic constraint and prove two structural non-existence results showing that separable and traveling-wave solutions cannot exist when this constraint is violated.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22556336

Author: huang, weiguang

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7210279766

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