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Volume 4,     Number 1,     Winter 1996

 

ON INVARIANT SOLUTIONS
OF NONLINEAR SCHRODINGER EQUATION
WITH VARIABLE COEFFICIENTS
O.P. BHUTANI, K. VIJAYAKUMAR AND M.H.M. MOUSSA

Abstract. The nonlinear Schrodinger equation iψt + a(t)ψxx + b(t)|ψ|²ψ = 0, with variable coefficients as indicated, is investigated for symmetries in generalized form and invariant solutions via group theoretic analysis. This has resulted in an integrability condition that is more general than the one reported in the literature. Furthermore, for four different forms of a(t) and b(t), the integrability condition is utilized to obtain subalgebras of the Lie algebra and invariant solutions. More specifically, six explicit solutions and three obtainable via Painleve PIV type equations, are presented.

 

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