Solution of the equation of transfer for interlocked multiplets by the method of Laplace transform and Winer-Hopf technique with planck function as a nonlinear function of optical depth

The equation of transfer for interlocked multiplets has been solved by Laplace transformation and the Wiener-Hopf technique developed by Dasgupta (1978) considering two nonlinear forms of Planck function: i.e., (a) $$B{text{ }}_{text{v}} (T) = B(t) = b_0 + b_1 {text{ }}e^{ - alpha t} ,$$ (b) $$B{text{ }}_{text{v}} (T) = B(t) = b_0 + b_1 t + b_2 E_2 (t).$$ Solutions obtained by Dasgupta (1978) or by Chandrasekhar (1960) may be obtained from our solutions by dropping the nonlinear terms.