ABSTRACT
Jump phenomena are concerned with large amplitude responses of nonlinear systems that are caused by small amplitude disturbances. This chapter describes some well-known physical problems where large jumps in the solution amplitude are important features of the response. It briefly outlines a new method that has been developed to solve certain jump problems. Dramatic examples of jump phenomena occur in the buckling of elastic shells. One of the oldest problems in which jump phenomena are a significant feature is for nonlinear electrical circuits or mechanical systems. The chapter discusses the method of rational functions which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter or, possibly, as functions of a rational function. The suitability of rational function representations follows from the fact that for some jump problems which can be solved explicitly, the solution is in the form of a rational function.
