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An auxiliary function used in Hirota's bilinear method to encode a solution of an integrable partial differential equation. Products and ratios of tau functions replace nonlinear field variables; their differential equations become bilinear. In a Sine-Gordon multisoliton tau representation, two real tau functions encode the field as a continuous $4\arg (f+ig)$.

An exact nonlinear-wave solution containing several localized solitons. In an integrable scattering solution, these objects approach separated incoming and outgoing profiles, with collision effects encoded by position shifts and internal phases. Bäcklund transformations and Hirota's bilinear method construct examples such as the Sine-Gordon multisoliton tau representation.