A restricted Bäcklund transformation

The Backlund transformation provides a mathematical tool which displays the interaction of solitons. Here a simple, systematic Backlund formalism is introduced which permits the explicit construction of these transformations for a restricted class of nonlinear wave equations. Traditionally a Backlund transformation has been viewed as a transformation of a solution surface of a partial differential equation into another surface which may not satisfy the same equation. In the present paper the term ``restricted Backlund transformation'' (hereafter abbreviated R‐B) is used to refer to the case in which the transformed surface does satisfy the same equation. This formalism clarifies the nature of those transformations which have already been used to study nonlinear interactions in many physical problems. The formalism is introduced through a form of the linear Klein‐Gordon equation. For this linear example a complete set of Fourier components is generated by a sequence of R‐B transformations. This concrete ex...

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