Geometric Analysis of Nonlinear Partial Differential Equations

• Other Authors: Lychagin, Valentin (Editor), Krasilshchik, Joseph (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute 2021
• Subjects: Research & information: general; Mathematics & science; adjoint-symmetry; one-form; symmetry; vector field; geometrical formulation; nonlocal conservation laws; differential coverings; polynomial and rational invariants; syzygy; free resolution; discretization; differential invariants; invariant derivations; symplectic; contact spaces; Euler equations; shockwaves; phase transitions; symmetries; integrable systems; Darboux-Bäcklund transformation; isothermic immersions; Spin groups; Clifford algebras; Euler equation; quotient equation; contact symmetry; optimal investment theory; linearization; exact solutions; Korteweg-de Vries-Burgers equation; cylindrical and spherical waves; saw-tooth solutions; periodic boundary conditions; head shock wave; Navier-Stokes equations; media with inner structures; plane molecules; water; Levi-Civita connections; Lagrangian curve flows; KdV type hierarchies; Darboux transforms; Sturm-Liouville; clamped; hinged boundary condition; spectral collocation; Chebfun; chebop; eigenpairs; preconditioning; drift; error control
• Online Access: DOAB: download the publication; DOAB: description of the publication

This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.