Some exact solutions of nonlinear chiral field equations

Some new exact solutions of the nonlinear field equations for the chiral invariant model of pion dynamics are presented here. These solutions are a further generalization of some previous works presented by one of the authors (Ray). It is interesting to note that equations in (3.2) obtained by Ray (1978) are conformally invariant. Hence from any solution of these equations one can immediately generate infinitely many other solutions of these equations simply by replacing (x 1, x 2) by ( y, z), where y and z are any two mutually conjugate solutions of Laplace’s equations. Further, a striking similarity in form of these equations with one of the two generalized Lund–Regge equations makes the study of the solutions of these equations more worthwhile with the view that the study of the solutions of these equations will eventually lead to the study of the solution of a larger class of equations that will include these equations and generalized Lund–Regge equations as special cases.