scholarly journals Weak transversality and partially invariant solutions

2003 ◽  
Vol 44 (6) ◽  
pp. 2704 ◽  
Author(s):  
A. M. Grundland ◽  
P. Tempesta ◽  
P. Winternitz
Keyword(s):  
Invariant Solutions ◽  
Partially Invariant Solutions

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

Lie subgroups of the symmetry group of the equations describing a nonstationary and isentropic flow: Invariant and partially invariant solutions

1994 ◽  
Vol 72 (7-8) ◽  
pp. 362-374 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Symmetry Group ◽  
Dimensional Space ◽  
Projective Group ◽  
Invariant Solutions ◽  
Partially Invariant Solutions ◽  
Isentropic Flow ◽  
Dimensional Space Time ◽  
Group A ◽  
Special Case

We study the symmetries of the equations describing a nonstationary and isentropic flow for an ideal and compressible fluid in four-dimensional space-time. We prove that this system of equations is invariant under the Galilean-similitude group. In the special case of the adiabatic exponent γ = 5/3, corresponding to a diatomic gas, the symmetry group of this system is larger. It is invariant under the Galilean-projective group. A representatives list of subalgebras of Galilean similitude and Galilean-projective Lie algebras, obtained by the method of classification by conjugacy classes under the action of their respective Lie groups, is presented. The results are given in a normalized list and summarized in tables. Examples of invariant and nonreducible partially invariant solutions, obtained from this classification, is constructed. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras for the Euler and magnetohydrodynamics equations.

A differential constraints approach to partial invariance

1995 ◽  
Vol 6 (6) ◽  
pp. 631-637 ◽  
Author(s):  
Jeffrey Ondich
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Invariant Solutions ◽  
Differential Constraints ◽  
Partially Invariant Solutions ◽  
Prandtl Equations ◽  
Partial Invariance ◽  
Special Case ◽  
Method Of Differential Constraints

Ovsiannikov's method of partially invariant solutions of differential equations can be considered to be a special case of the method of differential constraints introduced by Yanenko and by Olver and Rosenau. Differential constraints are used to construct non-reducible partially invariant solutions of the boundary layer or Prandtl equations.

scholarly journals Simple partially invariant solutions

2019 ◽  
Vol 11 (1) ◽  
pp. 90-99 ◽  
Author(s):  
Salavat Valeevich Khabirov
Keyword(s):  
Invariant Solutions ◽  
Partially Invariant Solutions
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