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We prove that the nonlinear Schr?dinger equation of attractive type (NLS+) describes just spherical surfaces (SS) and the nonlinear Schr?dinger equation of repulsive type (NLS-) determines only pseudospherical surfaces (PSS). This implies that, though we show that given two differential PSS (resp.
SS) equations there exists a local gauge transformation (despite of changing the independent variables or not) which transforms
a solution of one into any solution of the other, it is impossible to have such a gauge transformation between the NLS+ and the NLS-. 相似文献
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Science China Mathematics - We prove that the nonlinear Schrödinger equation of attractive type (NLS+) describes just spherical surfaces (SS) and the nonlinear Schrödinger equation of... 相似文献
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We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed. 相似文献
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