The concept of gauge transformation in soliton theory is introduced. It is shown that three different eigenvalue problems in 2×2 matrix form are connected by the gauge transformations. As an application of the theory, the interrelations among the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, isotropic Heisenberg equation and a new integrable equation are studied.
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Wadati et al. (1983) studied this question.
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