## Reduction of Systems of Nonlinear Partial Differential Equations to Simplified Involutive Forms (1996)

Citations: | 43 - 14 self |

### BibTeX

@MISC{Reid96reductionof,

author = {Gregory J. Reid and Allan D. Wittkopf and Alan Boulton},

title = {Reduction of Systems of Nonlinear Partial Differential Equations to Simplified Involutive Forms},

year = {1996}

}

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### Abstract

We describe the rif algorithm which uses a finite number of differentiations and algebraic operations to simplify analytic nonlinear systems of partial differential equations to what we call reduced involutive form. This form includes the integrability conditions of the system and satisfies a constant rank condition. The algorithm is useful for classifying initial value problems for determined pde systems and can yield dramatic simplifications of complex overdetermined nonlinear pde systems. Such overdetermined systems arise in analysis of physical pdes for reductions to odes using the Nonclassical Method, the search for exact solutions of Einstein's field equations and the determination of discrete symmetries of differential equations. Application of the algorithm to the associated nonlinear overdetermined system of 856 pdes arising when the Nonclassical Method is applied to a cubic nonlinear Schrodinger system yields new results. Our algorithm combines features of geometric involutiv...