Exact solutions for the fractional nonlinear Boussinesq equation

2023/03/08 by Andrea N. Ceretani, F. Falcini, Ceretani, A. +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2303.04775

openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the existence of exact solutions in closed form to a fractional version of the nonlinear Boussinesq equation for groundwater flow through an unconfined aquifer. We show this fractional equation appears naturally when the classical nonlinear Darcy's law is replaced by a space-fractional one. After a physical discussion on the fractional model, we give several exact solutions in closed form for special choices of initial and boundary data. We provide solutions for steady and unsteady cases, by considering both classical and fractional derivatives in time.

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