The geometry of differential constraints for a class of evolution PDEs

2016/07/31 by Francesco C. De Vecchi, Paola Morando · 7 citations
Economics, Econometrics and Finance · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Class (philosophy) #Computer science #Constructive #Differential Equations and Numerical Methods #Differential equation #Fluid Dynamics and Turbulent Flows #Integrable system #Isospectral #Mathematical analysis #Mathematics #Stochastic partial differential equation #Stochastic processes and financial applications #math-ph #math.MP #msc:35A30 #msc:35B06 #nlin.SI

paper · pdf · doi:10.1016/j.geomphys.2020.103771

published in Journal of Geometry and Physics 156, 103771 (Elsevier BV) · Revised abstract and introduction

arxiv created 2016/09/28 · openalex publication_date 2020/06/12 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in order to obtain explicit differential constraints for PDEs belonging to this family. Several examples, with applications in non-linear stochastic filtering theory, stochastic perturbation of soliton equations and non-isospectral integrable systems, are discussed in detail to verify the effectiveness of the method.

Citations

• Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
• Solvable structures for evolution PDEs admitting differential constraints
• Smooth Manifolds and Observables

Cited by

• Symmetries of stochastic differential equations using Girsanov transformations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps