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Table 1 Classification of f( w 0 x ) and λ( w 0 x ) with the corresponding extensions of Approx L P

From: Approximate symmetries in nonlinear viscoelastic media

Case

Forms of f( w 0 x ) and λ( w 0 x )

Extensions of Approx L P

I

f( w 0 x )= f 0 e 2 p w 0 x

X 8 =x x +( w 0 +px) w 0 +s w 1 w 1

λ( w 0 x )= λ 0 e 1 + s p w 0 x

II

f( w 0 x )= f 0 ( w 0 x + q ) 2 p

X 8 =x x +[(1+p) w 0 +pqx] w 0 +s w 1 w 1

λ( w 0 x )= λ 0 ( w 0 x + q ) 1 + s p 1

  1. f 0 , λ 0 , p, q and s are constitutive constants with p ≠ 0.