Algorithmic computation of generalized symmetries of nonlinear evolution and lattice equations |
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Authors: | Ünal Gökta? Willy Hereman |
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Institution: | (1) Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401‐1887, USA |
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Abstract: | A straightforward algorithm for the symbolic computation of generalized (higher‐order) symmetries of nonlinear evolution equations
and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the
polynomial form of the generalized symmetries. The coefficients of the symmetry can be found by solving a linear system. The
method applies to polynomial systems of PDEs of first order in time and arbitrary order in one space variable. Likewise, lattices
must be of first order in time but may involve arbitrary shifts in the discretized space variable.
The algorithm is implemented in Mathematica and can be used to test the integrability of both nonlinear evolution equations
and semi‐discrete lattice equations. With our Integrability Package, generalized symmetries are obtained for several well‐known
systems of evolution and lattice equations. For PDEs and lattices with parameters, the code allows one to determine the conditions
on these parameters so that a sequence of generalized symmetries exists. The existence of a sequence of such symmetries is
a predictor for integrability.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | symmetry integrability evolution equation lattice PDE DDE 35Q53 35R10 34K99 68Q40 |
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