integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system...

System integration is defined in engineering as the process of bringing together the component sub-systems into one system (an aggregation of subsystems...

and when this works out in the whole phase space M the dynamical system is integrable. In most cases the patch cannot be extended to the entire phase space...

A systems integrator (or system integrator) is a person or company that specializes in bringing together component subsystems into a whole and ensuring...

approach to certain over-determined systems, for example, including Lax pairs of integrable systems. A Pfaffian system is specified by 1-forms alone, but...

A rail integration system (RIS; also called a rail accessory system (RAS), rail interface system, rail system, mount, base, gun rail, or simply a rail)...

the Gelfand–Zeitlin system (also written Gelfand–Zetlin system, Gelfand–Cetlin system, Gelfand–Tsetlin system) is an integrable system on conjugacy classes...

equations). The classical Gaudin models are integrable. They are also a specific case of Hitchin integrable systems, when the algebraic curve that the theory...

System integration testing (SIT) involves the overall testing of a complete system of many subsystem components or elements. The system under test may...

In mathematics, the Hitchin integrable system is an integrable system depending on the choice of a complex reductive group and a compact Riemann surface...

equation or a system of differential equations: Integrability conditions for differential systems Integrable system Order of integration, in statistics...

The Central American Integration System (Spanish: Sistema de la Integración Centroamericana, or SICA) has been the economic and political organization...

studied in the two-dimensional case as an integrable system, in particular an integrable field theory. Its integrability was shown by Faddeev and Reshetikhin...

Lebesgue integral Liouville-integrability Darboux-integrability Integrable system (mathematics, physics) System integration (information technology) Interoperability...

equivalent to the Riemann integral. A function is Darboux-integrable if and only if it is Riemann-integrable. Darboux integrals have the advantage of being easier...

coordinates. A Hamiltonian system which is integrable is referred to as 'integrable in the Liouville sense' or 'Liouville-integrable'. Famous examples are...

terms of trajectories in phase space of an integrable Hamiltonian system. The motion of an integrable system is confined to an invariant torus (a doughnut-shaped...

The core idea of artificial intelligence systems integration is making individual software components, such as speech synthesizers, interoperable with...

are an important ingredient in the modern mathematical theory of integrable systems, and have numerous applications in a variety of other domains. They...

Operators and Integrable Hierarchies" "[1]" Cárdenas, Marcela; Correa, Francisco; Lara, Kristiansen; Pino, Miguel (2021-10-12). "Integrable Systems and Spacetime...

because it is one of the earliest examples of a non-linear completely integrable system. It is given by a chain of particles with nearest neighbor interaction...

typically arise when considering slowly modulated long waves of an integrable dispersive PDE system. The dispersionless Kadomtsev–Petviashvili equation (dKPE)...

Integrable algorithms are numerical algorithms that rely on basic ideas from the mathematical theory of integrable systems. The theory of integrable systems...

and is an example of an integrable PDE. Among well-known integrable PDEs, the sine-Gordon equation is the only relativistic system due to its Lorentz invariance...

manifold is integrable (or involutive) if and only if it arises from a regular foliation. In this context, the Frobenius theorem relates integrability to foliation;...

theory' for integrable systems is the anti-self-dual Yang–Mills (ASDYM) system. Ward's conjecture is the conjecture that in fact all integrable ODEs or PDEs...

are an important tool in soliton theory and integrable systems. A Bäcklund transform is typically a system of first order partial differential equations...

Ovsienko, R.E. Schwartz, S.Tabachnikov, "The Pentagram Map: A Completely Integrable System", Communications in Mathematical Physics (2010) Spherical CR Geometry...

of the base of complex completely integrable system. The total phase of this complex completely integrable system can be identified with the moduli space...

completely integrable system. Such a collection of constants of motion are said to be in involution with each other. For a closed system (Lagrangian...