This is the abstract of the paper
  "A multidimensional superposition principle: classical solitons I"
by A. Alexeyev.

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Abstract: A new concept, the multidimensional superposition principle, is
proposed for differential equations. In its frameworks classical soliton
interactions can easily be explained and described, and other wave
structures (`soliton structures') with more complex and intriguing
properties are predicted.

The case of nonlinear PDEs associated with the Riccati equations via
singular manifold expansions is considered in details. The possibility of
the existence for the KdV-type soliton/kink is shown for them. Moreover,
the cases with unelastic interactions are also demonstrated for the
specific conditions.

The above approach can be applied to naturally construct solutions of
ordinary and partial differential equations as well. As such an example,
some rational, soliton-rational, and two-soliton solutions were obtained
for the KdV equation.