Integral Transforms Associated with Some Nonlinear Partial Differential Equations. Linked Operatorial Formulations

摘要

Previouly considered T, T tilde integral transforms connecting general solutions of some nonlinear partial differential equations and associated pairs of linear systems are examined with further details. New illustrative examples concerning 2+1 modified Kadomtsev-Petviashvili equations and 1+1 reductions are examined. It is emphasised that, whatever is the case, the T (resp. T tilde) are defined through the same type of integral expressions, concise operatorial forms of which are given. A comparison is made between two types of reductions implicated in the reviewed examples. For completeness, L, L tilde transformations linked with the T, T tilde and also connecting solutions of the linear systems, are introduced. (ERA citation 11:052732)