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integrab
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There are 8 letters in INTEGRAB ( A1B3E1G2I1N1R1T1 )
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Definitions of integrab in various dictionaries:
INTEGRAB - In the context of differential equations to integrate an equation means to solve it from initial conditions. Accordingly, an integrable system is a ...
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In the context of differential equations to integrate an equation means to solve it from initial conditions. Accordingly, an Integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions. * Many systems of differential equations arising in physics are integrable. A standard example is the motion of a rigid body about its center of mass. This system gives rise to a number of conserved quantities: the angular momenta. Conserved quantities such as these are also known as the first integrals of the system. Roughly speaking, if there are enough first integrals to give a coordinate system on the set of solutions, then it is possible to reduce the original system of differential equations to an equation that can be solved by computing an explicit integral. Other examples giving rise to integrable systems in physics are some models of shallow water waves (Korteweg–de Vries equation), the nonlinear Schrödinger equation, and the Toda lattice in statistical mechanics. * While the presence of many conserved quantities is generally a fairly clear-cut criterion for integrability, there are other ways in which integrability can appear. It is famously difficult to be precise about what the term means. Nigel Hitchin (Hitchin, Segal & Ward, p. 1) draws a comparison to a quotation by jazz musician Louis Armstrong, who when asked what jazz was, is rumored to have replied "If you gotta ask, you'll never know." Hitchin identifies three generally recognizable features of integrable systems: * the existence of many conserved quantities * the presence of algebraic geometry * the ability to give explicit solutions |