Results 71 to 80 of about 58,877 (128)

The shallow water equations: conservation laws and symplectic geometry

International Journal of Mathematics and Mathematical Sciences, 1987
We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations.
Yilmaz Akyildiz
doaj   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

The sharp energy-capacity inequality on convex symplectic manifolds

, 2019
In symplectic geometry, symplectic invariants are useful tools in studying symplectic phenomena. Hofer-Zehnder capacity and displacement energy are important symplectic invariants. Usher proved the so-called sharp energy-capacity inequality between Hofer-
Sugimoto, Yoshihiro
core  

Extrapolation Boundary Conditions for 2‐D Smoothed Particle Hydrodynamics

International Journal for Numerical Methods in Fluids, Volume 97, Issue 9, Page 1248-1279, September 2025.
This paper introduces novel inflow, outflow, and wall boundaries for the WCSPH method. Utilising innovative concepts from finite volume methods, fluid properties of sequential dynamic particles with varying distances to boundaries are extrapolated to ghost and wall particles using first‐order Taylor series expansion.
Hossein Mahdizadeh, Colin D. Rennie, Benedict D. Rogers, Abolghasem Pilechi   +3 more
wiley   +1 more source

Stochastic Multisymplectic PDEs and Their Structure‐Preserving Numerical Methods

Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.
ABSTRACT We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637].
Ruiao Hu, Linyu Peng
wiley   +1 more source

Discrete dynamics and supergeometry

Journal of High Energy Physics
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and naturally incorporates laboratories.
Subhobrata Chatterjee, Andrew Waldron, Cem Yetişmişoğlu   +2 more
doaj   +1 more source

Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain

Journal of Applied Mathematics, 2011
The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as ...
Xiao-Chuan Li, Wei-An Yao
doaj   +1 more source

Exponential actions defined by vector configurations, Gale duality, and moment‐angle manifolds

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2571-2629, September 2025.
Abstract Exponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non‐Kähler complex geometry, toric geometry and topology. These include leaf spaces of holomorphic foliations, intersections of real and Hermitian quadrics, the quotient construction of simplicial toric ...
Taras Panov
wiley   +1 more source

Locally conformal symplectic manifolds

International Journal of Mathematics and Mathematical Sciences, 1985
A locally conformal symplectic (l. c. s.) manifold is a pair (M2n,Ω) where M2n(n>1) is a connected differentiable manifold, and Ω a nondegenerate 2-form on M such that M=⋃αUα (Uα- open subsets). Ω/Uα=eσαΩα, σα:Uα→ℝ, dΩα=0.
Izu Vaisman
doaj   +1 more source

Differential Invariants of Measurements, and Their Relation to Central Moments

Entropy, 2020
Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of V×V*×R. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central ...
Eivind Schneider
doaj   +1 more source