This letter demonstrates nonlinear realizations of W^2_3 algebra, uncovering its implications for the Boussinesq equation and Toda lattice.
In this letter we consider the nonlinear realizations of the classical Polyakov's algebra W^(2)_3. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with intercharged space and evolution coordinates. By adding one more space coordinate and introducing two copies of the W^(2)_3 algebra, the same method yields the sl(3,R) Toda lattice equations.
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S. et al. (1994) studied this question.
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