## 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:

 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations)
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