Triadis, Dimetre; Broadbridge, Philip; Kajiwara, Kenji; Maruno, Ken-ichi Integrable discrete model for one-dimensional soil water infiltration. (English) Zbl 1398.35181 Stud. Appl. Math. 140, No. 4, 483-507 (2018). Summary: We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection-diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time-dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self-adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost. MSC: 35Q35 PDEs in connection with fluid mechanics 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 76T20 Suspensions 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:soil water infiltration; Burgers equation PDFBibTeX XMLCite \textit{D. Triadis} et al., Stud. Appl. Math. 140, No. 4, 483--507 (2018; Zbl 1398.35181) Full Text: DOI arXiv