Abstract
Let (E): u t=H(u) denote the KdV, MKdV or Burgers equation, and U(s)=Σ(Dj s)∂/∂u j, where D=d/dx, u i=Di u, s=s(u, u 1, ..., u n) is a polynomial of u i with constant coefficients, be the generator of invariant group of equation (E). We prove in this paper that all such generators form a commutative Lie algebra, from which it follows that for any symmetry s(u, ..., u n) of (E), the evolution equation u t=s(u, ..., u n) possesses an infinite number of symmetries (or conservation laws in the case of KdV and MKdV equations).
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Gue-Zhang, T. The lie algebra of invariant group of the KdV, MKdV, or Burgers equation. Lett Math Phys 3, 387–393 (1979). https://doi.org/10.1007/BF00397212
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DOI: https://doi.org/10.1007/BF00397212