Abstract
Gauge transformations constructed by means of the Jost solutions related to two similar cases of the quadratic bundle of general form are studied. Those transformations are taken at arbitrary fixed point λ=λ0 of the continuous spectrum of the problem. The entire class of gauge-equivalent nonlinear evolution equations (NLEE) and their Hamiltonian structures are obtained. An interesting case of reduction of the potential is examined. It was shown that the entire class of NLEE splits into three different (in terms of coefficient functions) subclasses of gauge-equivalent NLEE. The gauge equivalence between the derivative nonlinear Schrödinger equation and some modifications of the derivative Landau–Lifshitz equation (DLLE) is demonstrated. The simplest soliton solutions of the DLLE and its higher analogs are obtained.
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