A combination of Yang's
equations for SU(2) gauge fields and Charap's equations for pion dynamics
with exact solutions
SUSANTO CHAKRABORTY and PRANAB KRISHNA CHANDA*
Central Drugs Laboratory, 3 Kyd Street, Calcutta
700 016, India
*Govt. Teacher's Training College, Malda 732 101, India
Abstract:
Two sets of nonlinear partial differential equations
originating from two different physical situations have been combined and a new set of
nonlinear partial differential equations has been formed wherefrom the previous two sets
can be obtained as particular cases. One of the two sets of equations was obtained by Yang
[1] while discussing the condition of self-duality of SU(2) gauge fields on
Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral
invariant model of pion dynamics under tangential parametrization. Using the same type of
ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two
sets of equations. Here exact solutions of the combined set of equations with particular
values of the coupling constants have been obtained for a similar ansatz. These solutions
too are physical in nature.
keywords: Exact solutions; combined field equations; SU(2)
gauge field; self duality; pion dynamics; chiral invariance.
pacs : 11.30; 11.10
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