The resulting solution takes the form:

f2 (y,T,V,Vo)_n0{exp -ik(y-t)-(! +'))k(n + no)coth((1 + i)

x Io

x Io

where C.C. denotes the complex conjugate term. This function is shown in Fig. 2.17.1.

Fig. 2.17.1. The space distribution f2(y,T) in the second approximation in the interval t = 0.3-1.3 for 6 = 0.1, 6o = 0. According to Dorman, Shakhov and Stehlik (2003).

Let us consider the Eq. 2.17.5 in the non-zero but small time limit t ^ 0. Then the expression for f2(x,t,8,8o) acquires the form analogous to Eq. 2.17.2 obtained in the first order approximation:

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