Abstract
where q, r, and s are physical observables, x and t representing spaceand time-like independent variables. Taking q 1⁄4 Z, r 1⁄4 X þ iY , and s 1⁄4 X iY with i 1⁄4 1, eq. (4) is transformed to eq. (1) provided 1⁄4 xþ t and 1⁄4 x t. Singularity structure analysis of eq. (4) has recently been investigated. The associated Backlund transformation has been constructed and Hirota’s bilinearization also given through dependent variable transformations. As a result, q, r, and s are expressed as follows r 1⁄4 G=F; s 1⁄4 H=F; q 1⁄4 2@tðlnFÞ: ð5Þ We assume r 1⁄4 s, ð?Þ denoting complex conjugation, and we transform eq. (5) to a new one by looking for some soliton solutions with the following asymptotic behavior jrj ! 0; q ! x; as jxj ! 1: ð6Þ We may then write
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