scholarly journals Thick slab punching with symmetry reductions

2020 ◽  
Vol 21 (3) ◽  
pp. 875-889 ◽  
Author(s):  
Lennart Bocklenberg ◽  
Peter Mark
Keyword(s):  
Thick Slab ◽  
Symmetry Reductions

RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION

2008 ◽  
Vol 06 (04) ◽  
pp. 349-369 ◽  
Author(s):  
PETER A. CLARKSON
Keyword(s):  
Infinite Number ◽  
Boussinesq Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Rational Solutions ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Symmetry Reductions ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

Continuous symmetries of the discrete nonlinear telegraph equation

1999 ◽  
Vol 10 (3) ◽  
pp. 265-284 ◽  
Author(s):  
M. S. ODY ◽  
A. K. COMMON ◽  
M. I. SOBHY
Keyword(s):  
Initial Data ◽  
Difference Equations ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
Lie Symmetries ◽  
Discrete Equation ◽  
Symmetry Reductions ◽  
Nonlinear Telegraph Equation ◽  
Continuous Symmetries

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

Coloring variants of the Re3B type

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Stefan Seidel ◽  
Rainer Pöttgen
Keyword(s):  
Basic Structure ◽  
Crystal Chemical ◽  
Space Group ◽  
Type Space ◽  
Symmetry Reductions ◽  
Phase Precipitate ◽  
Lower Symmetry ◽  
Trigonal Prisms

Abstract The Re3B type, space group Cmcm, has boron-centered trigonal prisms as central building units and is one of the basic structure types with numerous binary and ternary representatives. The coloring of different atoms on the two crystallographically independent rhenium sites leads to a manifold of compounds with different bonding peculiarities that are rather isopointal than isotypic with the prototype. Typical compounds are the S-phase precipitate MgCuAl2, the silicide ScPt2Si or the iodide Th0.5Pb0.5I3 (PuBr3 type). Differences in size or composition might force symmetry reductions. This is discussed for YZn3 (space group Pnma) and the different coloring variants ScRhSi2 and TaNi2P which show different twists of the trigonal prisms. Striking singular representatives with lower symmetry structures are BaThBr6 (Pmma) and NbCo2B (P21/c) which allow different ordering/distortion patterns for the prisms. All these crystal chemical details are discussed on the basis of group subgroup schemes (Bärnighausen trees).

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