Schrodinger equation and wave equation on finite graphs
Li Ma, X. Y. Wang
TL;DR
This paper investigates the solutions of Schrödinger and wave equations on finite graphs, providing explicit formulas, energy conservation laws, and discussing applications to nonlinear variants.
Contribution
It introduces explicit solution formulas and energy conservation results for Schrödinger and wave equations on finite graphs, extending classical PDE analysis to discrete structures.
Findings
Explicit solutions for equations on finite graphs
Energy conservation laws established
Applications to nonlinear problems discussed
Abstract
In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated.
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Taxonomy
TopicsGraph theory and applications · Limits and Structures in Graph Theory · advanced mathematical theories