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This paper will study Eckhaus-Kundu equation from the perspective of Lie symmetry analysis. We will systematically construct similarity reductions in order to perform the explicit invariant solutions of this version of the nonlinear Schrödinger equation with nonlinear dispersion and cubic-quintic nonlinearities, describing the propagation of ultrashort pulses in optical fibers. Some new wave solutions with real and imaginary parts of trigonometric type or of a compound of trigonometric and hyperbolic types will be pointed out. [ABSTRACT FROM AUTHOR]