scholarly journals A New Class of Exact Solutions to a Generalized form of Charap’s Nonlinear Chiral Field Equations of Field Theory

2017 ◽  
Vol 14 (3) ◽  
pp. 417-426
Author(s):  
Indranil Mitra ◽  
◽  
Pranab Krishna Chanda
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Chiral Field ◽  
Field Equations ◽  
New Class

Some exact solutions of nonlinear chiral field equations

1984 ◽  
Vol 25 (8) ◽  
pp. 2557-2562 ◽  
Author(s):  
Pranab Krishna Chanda ◽  
Dipankar Ray ◽  
Utpal Kumar De
Keyword(s):  
Exact Solutions ◽  
Chiral Field ◽  
Field Equations

SOLUTIONS FOR THE SU(2) CHIRAL FIELD EQUATIONS WITHOUT SPATIAL SYMMETRY

1989 ◽  
Vol 04 (20) ◽  
pp. 1915-1922
Author(s):  
HANS J. WOSPAKRIK
Keyword(s):  
Harmonic Function ◽  
Exact Solutions ◽  
Harmonic Mappings ◽  
Chiral Field ◽  
Field Equations ◽  
Spatial Symmetry ◽  
Affine Parameter ◽  
Dimensional Spacetime

Some exact solutions for the SU(2) chiral field equations in the Euclidean and Minkowskian four dimensional spacetime without spatial symmetry are presented. This is achieved by using the harmonic mappings method. Precisely, these solutions correspond to the geodesics of the 3-sphere S3, where the affine parameter is a harmonic function of spacetime.

scholarly journals Some nozzle flows found by the hodograph method

1959 ◽  
Vol 1 (1) ◽  
pp. 80-94 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Exact Solutions ◽  
Two Dimensions ◽  
Nozzle Design ◽  
Perfect Gas ◽  
Field Equations ◽  
Rigid Boundary ◽  
Hodograph Method ◽  
Isentropic Flow ◽  
Fixed Boundaries ◽  
Nozzle Flows

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

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