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Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation. (English) Zbl 1089.81019
Summary: By using Lie’s invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra $\mathcal E_{\chi_0}$. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations which can be mapped, by means of an equivalence transformation of $\mathcal E_{\chi_0}$, to the well-known cubic Schrödinger equation. We also provide the explicit form of the transformation.

MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q55NLS-like (nonlinear Schrödinger) equations
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