A Remark of the Sanders-Wang's Theorem on Symmetry-integrability

2005/03/30 by Lizhou Chen, Chen, Lizhou
Mathematics · Physics and Astronomy · #35A30 #37K05 #37K10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35A30 #msc:37K05 #msc:37K10

paper · pdf · doi:10.48550/arxiv.math-ph/0503070

contents changed, 11 pages

arxiv created 2005/11/10 · arxiv updated 2009/12/01

Abstract

We extend the integrability analysis for scalar evolution equations of type u_t=u_m+f(u,u₁,...,u_m-1) from the case that the right hand side is a λ-homogeneous formal power series to the case that it is a nonhomogeneous formal power series. It is proved that the existence of one nontrivial symmetry implies the existence of infinitely many, more precisely, the orders of the infinite integrable hierarchy must be one of the following cases: ℤ₊+1, 2ℤ₊+1, 6ℤ₊±1, or 6ℤ₊+1. Moreover, if the nonlinear part of the equation is a polynomial of order less than m-1, we show that any generalized symmetry is also of polynomial type.

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