Construction and simulation of discrete integrable model for soil water infiltration problem

Prof. Kenji Kajiwara (Institute of Mathematics for Industry, Kyushu University, Japan)
Title: Construction and simulation of discrete integrable model for soil water infiltration problem
Abstract: In this talk, we propose an integrable model and its discretization describing one-dimensional soil water infiltration problem. The model is formulated as the nonlinear boundary value problem for a nonlinear diffusion-convection equation, which is transformed to the Burgers equation by a certain independent variable transformation incorporating the dependent variable, called the hodograph transformation or the reciprocal transformation. We construct the discrete model preserving the underlying integrability nature and formulate it as the self-adaptive moving mesh scheme. If we require the numerical stability and high-precision coincidence with the special case where the exact solution is obtained, we need some investigation and modification of the discrete model from the point of view different from integrability. We discuss this point and show some numerical results.
This talk is based on the paper arXiv:1705.03129 by D. Triadis (Kyushu/La Trobe) , P. Broadbridge (La Trobe), K. Maruno (Waseda) and myself.

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