推广的$K(m,n,p)$方程的对称不可积性
Symmetry nonintegrability for extended $K(m,n,p)$ equation
摘要：
本文研究了扩展的$K(m,n,p)$方程$$ u_t=a(u^p)_{xxxxx}+b(u^n)_{xxx} + c(u^m)_{x} + f(u), $$的对称性，其中$a,b,c$为任意实常数，$m,n,p$为任意整数，证明了对于$a\neq 0$和$p\neq 1,-4$，该方程不存在阶数大于5的广义对称性，因而不是对称可积的.
英文摘要：
In the present paper we study symmetries of extended $K(m,n,p)$ equation $$ u_t=a(u^p)_{xxxxx}+b(u^n)_{xxx} + c(u^m)_{x} + f(u), $$ where $a,b,c$ are arbitrary real constants and $m,n,p$ are arbitrary integers, and prove that for $a\neq 0$ and $p\neq 1,-4$ this equation has no generalized symmetries of order greater than five and hence is not symmetry integrable.
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