ABSTRACT

This is a special case of equation 15.1.3.5 with n = 4.

3. ∂w

∂t = a

∂w

∂x4 + (bx + c)

∂w

∂x + f(w).

1◦. Suppose w(x, t) is a solution of this equation. Then the function

w1 = w(x + C1e-bt, t + C2),

where C1 and C2 are arbitrary constants, is also a solution of the equation.

2◦. Generalized traveling-wave solution: