ABSTRACT
Linearized Korteweg-de Vries equation.
1◦. Particular solutions of the homogeneous equation with Φ(x, t) = 0:
w(x, t) = a(x3 − 6t) + bx2 + cx+ k, w(x, t) = a(x5 − 60x2t) + b(x4 − 24xt), w(x, t) = a sin(λx+ λ3t) + b cos(λx+ λ3t) + c,
w(x, t) = a sinh(λx− λ3t) + b cosh(λx− λ3t) + c, w(x, t) = exp
(−λ3t)[a exp(λx)+ b exp(− 12λx) sin(√32 λx+ c)], where a, b, c, k, and λ are arbitrary constants.
