First integrals of the equations ofnon-linear wave dynamics

In algorithm for binding the first integrals of fourth-order non-linear differential equations, encountered when describing non-linearwave processes, is process, is proposed. The use of the method is illustrated by a number of examples. The first integrals obtained are employed to construct a solution of the generalized fifth-order Korteweg-de Vries equation in travelling-wave variables, which is expressed in terms of hyperelliptic integrals.