ABSTRACT
This is a special case of equation 7.4.1.1 with f (w) = awn. 1◦. Suppose w(x, t) is a solution of the equation in question. Then the functions
w1 = C 2 1w ( ±Cn-11 x + C2, ±C
) ,
w2 = w(x cosh λ + t sinh λ, x sinh λ + t cosh λ),
where C1, C2, C3, and λ are arbitrary constants, are also solutions of the equation (the plus or minus signs are chosen arbitrarily). 2◦. Solutions:
w(x, t) = b(x + C1t + C2) 21-n , b = [ 2(1 + n)(C21 – 1) a(1 – n)2
;
w(x, t) = [k(t + C1)2 – k(x + C2)2] 11-n , k = 14a(1 – n)2, where C1 and C2 are arbitrary constants.
