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Examples of the investigation of differential equations with modularized programs. (English) Zbl 0881.34001

The use of the REDUCE program CRACK for the symbolic integration and analysis of nonlinear differential equations is demonstrated on the basis of six examples: (i) determination of conservation laws of the Ito system and Fisher’s equation, (ii) determination of the Lie symmetry algebra of a unified field theory, (iii) computing finite transformations from the infinitesimal symmetry generators of an ordinary differential equation stemming from general relativity, (iv) solving a quasi-linear partial differential equation arising in the normal form theory of vector fields, (v) solving the Killing equations of the Kimura metric, and (vi) finding a Lagrangian for the Painlevé VI equation.

MSC:

34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
35C05 Solutions to PDEs in closed form
35N10 Overdetermined systems of PDEs with variable coefficients
35Q75 PDEs in connection with relativity and gravitational theory
68W30 Symbolic computation and algebraic computation
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References:

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