### Table 4.1. Additional de ning equations and nondegeneracy conditions for slow shock waves.

1996

Cited by 9

### Table 4.3. Additional de ning equations and nondegeneracy conditions for overcompressive shock waves.

1996

Cited by 9

### Table 2.2. Additional de ning equations and nondegeneracy conditions for slow shock waves.

### Table 2.4. Additional de ning equations and nondegeneracy conditions for transitional shock waves.

### Table 2.2. Additional de ning equations and nondegeneracy conditions for slow shock waves.

### Table 2.4. Additional de ning equations and nondegeneracy conditions for transitional shock waves.

### Table 4.1. Additional de ning equations and nondegeneracy conditions for slow shock waves.

### Table 4.3. Additional de ning equations and nondegeneracy conditions for overcompressive shock waves.

### Table 8. If the nondegeneracy conditions are satis ed we can draw a number of conclusions from this table. 1. Any one of the axial solution branches can bifurcate supercritically to produce a stable solution. 2. If the super squares and anti-squares are neutrally stable at cubic order, then one and only one of these two states bifurcates stably.

"... In PAGE 16: ... Thus the repeated eigenvalue, 12Tr(A), is simply 2@gi 1 @y1 . The details of the computations of the eigenvalues for the remaining axial planforms are omitted but the results are summarised in the second column of Table8 . Note that symmetry considerations alone determine that the eigenvalues of Dg are real for all of the axial planforms.... In PAGE 16: ... From the leading order terms in the equivariant bifurcation problem (4.4), and the expressions for the eigenvalues given in the second column of Table8 , the signs of the eigenvalues of Dg at bifurcation may be determined. Provided the nondegeneracy condition, b1 + b2 6 = 0; (4.... In PAGE 17: ...Table8 : Eigenvalues and their multiplicities for axial planforms associated with 8-dim. repre- sentations of ?s.... ..."

### Table 8: Eigenvalues and their multiplicities for axial planforms associated with 8-dim. repre- sentations of ?s. The coe cients a1; a2; a3; a4; b1; b2 are de ned by equations 4.4 and 4.5. Axial Planform and Eigenvalues Signs of Non-zero Branching Equation Eigenvalues

"... In PAGE 16: ... Thus the repeated eigenvalue, 12Tr(A), is simply 2@gi 1 @y1 . The details of the computations of the eigenvalues for the remaining axial planforms are omitted but the results are summarised in the second column of Table8 . Note that symmetry considerations alone determine that the eigenvalues of Dg are real for all of the axial planforms.... In PAGE 16: ... From the leading order terms in the equivariant bifurcation problem (4.4), and the expressions for the eigenvalues given in the second column of Table8 , the signs of the eigenvalues of Dg at bifurcation may be determined. Provided the nondegeneracy condition, b1 + b2 6 = 0; (4.... In PAGE 16: ...16) are satis ed. The results for all the axial planforms are summarized in the third column of Table8 . If the nondegeneracy conditions are satis ed we can draw a number of conclusions from this table.... ..."