Journal of Nonlinear Mathematical Physics 1998, V.5, N 4, 364–370. Letter Differential Constraints Compatible with Linearized Equations (original) (raw)
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints. One of the standard ways for determining particular solutions to partial differential equations is to reduce them to ordinary differential equations which are easier to solve. The classical work of Lie about group-invariant solutions generalizes well-known methods for finding similarity solutions and other basic reduction methods [1]. Bluman and Cole [2] proposed a generalization of Lie’s method for finding group-invariant solutions, which they named the “nonclassical ” method. In this approach, one replaces the condition for the invariance of the given system of differential equations by the weaker condition for the invariance of the combined system consisting of the original differential equations along with the equations requiring the group invariance of the solutions. P.J. Olver and P. Rose...