Abstract
Frobenius integrable decompositions are introduced for partial differential equations. Then, such integrable decompositions are generalized, which are applied to (2+1)-dimensional partial differential equations. Some generalized soliton equations are obtained which possess generalized Frobenius integrable decompositions, such as (2+1)-dimensional KdV equation, (2+1)-dimensional Burgers equation, (2+1)-dimensional dispersion equation, etc. Meanwhile, their special cases are just well-known KdV equation, Burgers equation, fifth-order dispersion equation, etc.
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