# auxiliary equation

## auxiliary equation

[ȯg¦zil·yə·re i′kwā·zhən]
(mathematics)
The equation that is obtained from a given linear differential equation by replacing with zero the term that involves only the independent variable. Also known as reduced equation.
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Xia, "A generalized auxiliary equation method and its application to (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations," Journal of Physics A-Mathematical and Theoretical, vol.
Zhang: A generalized new auxiliary equation method and its application to the (2 + 1)-dimensional breaking soliton equations, Appl.
The substitution z = w - 3p/w transforms this equation into an auxiliary equation [w.
The auxiliary Equation (2), coupled with the linearity assumption, Equation (3), on the other hand, estimates the effect of study time alone from boys in the class ([J.
19 Formal tests to determine whether a control equation is "necessary" are based on the function values obtained under the restriction that the error of an auxiliary equation is uncorrelated with the errors of the other equations in the system.
For each additional variable for which an expectation appears in FRB/US, an auxiliary equation, which expresses the variable as a function of its own past values and of the set of explanatory variables appearing in the core equations, is added to the forecasting model.
A key contribution of the paper is the modeling of the perception of earthquake risk by a proxy variable and auxiliary equation that includes indicators of susceptibility to earthquake damage, geographic location, and housing characteristics.
3) The direct comparison of these three models is carried out using true ex ante forecasts of money growth rather than an ex post decomposition of money growth into an anticipated and an unanticipated part by way of the frequently-used auxiliary equation approach.
The present work is motivated by the desire to establish an auxiliary equation method to construct new and more general exact solutions of variable-coefficient NPDEs, such as soliton and soliton-like solutions, triangular periodic solutions, Jacobi elliptic function solutions, and many exact explicit solutions in form of hyperbolic function solutions and trigonometric function solutions.

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