Scalar second-order evolution equations possessing an irreduciblesl2-valued zero-curvature representation

Scalar second order evolution equations possessing an irreducible sl2-valued zero curvature representation

We find all scalar second order evolution equations possessing an sl2-valued zero curvature representation that is not reducible to a proper subalgebra of sl2. None of these zero-curvature representations admits a parameter. For more than twenty years, researchers are being attracted by the problem of classification of nonlinear systems possessing a zero-curvature representation (ZCR). Efforts ...

Scalar second order evolution equations possessing an irreducible sl2-valued zero curvature representation by

We find all scalar second order evolution equations possessing an sl2-valued zero curvature representation that is not reducible to a proper subalgebra of sl2. None of these zero-curvature representations admits a parameter. For more than twenty years, researchers are being attracted by the problem of classification of nonlinear systems possessing a zero-curvature representation (ZCR). Efforts ...

Strongly hyperbolic second order Einstein’s evolution equations

BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudodifferential first order reduction of these equations is strongly hyperbolic. In ...

Boolean-Valued Second-Order Logic

Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows (λt = λ , l ≥ 0) from the discrete spectral problem associated with a give...