A novel Backlund invariance of a nonlinear differential equation

[摘要] Here the nonlinear ordinary differential equation yyS(x) is investigated. The interest of the proposed study is twofold: indeed, the high nonlinearity exhibited by the considered equation does not allow the application of any linearization method; on the other hand, it turns out, under suitable conditions, to be equivalent to a nonlinear integral equation arising in extended kinetic theory. The equivalence between the two nonlinear problems is exploited; in particular, conditions which need to be prescribed to establish such an equivalence are considered. Backlund transformations are applied to study the problem of interest. Specifically, it is proved that the nonlinear differential equation enjoys an invariance property when the source term S(x) is represented by a solution of a suitable functional equation. The latter is discussed and some solutions are explicitly written; thus, the corresponding Backlund charts are depicted to show the obtained new invariances. (C) 2000 Academic Press.

[发布日期] 2000-12-15

[关键词] nonlinear ordinary differential equations;Backlund transformations;invariance properties