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The integrability conditions of nonautonomous Hirota equation are given by using Painlevé, Lax pair and similarity transformation methods. When compared with these methods, the Lax pair method allows for the dispersion, nonlinearity, and dissipation coefficients t-dependent, while the Painlevé analysis restrict to be t-independent. The integrability conditions of the Painlevé analysis method is a...
A systematic investigation to derive the Lax pair and group theoretical properties of deformed N-coupled nonlinear Schrödinger equations (N-coupled NLS) is presented. Exploiting the obtained Lie point symmetries, the corresponding similarity reductions for $$N =1$$ N = 1 and $$N = 2$$ N = 2 are derived separately and show that each of them passes the Painlevé property of ordinary...
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