Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation. (English) Zbl 1089.81019

Senthilvelan, M.; Torrisi, M.; Valenti, A.

J. Phys. A, Math. Gen. 39, No. 14, 3703-3713 (2006).

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)