【摘 要】
：
The nonlinear Schr(o)odinger equation (NLS) is a widely applicable model for wave packets dynamics [1].For wave propagation in aninhomogeneous medium, e.g.a
【机 构】
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DepartmentofMechanicalEngineering,TheUniversityofHongKong,PokfulamRoadHongKong
【出 处】
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International Conference Nonlinear Waves-Theory and Applicat
论文部分内容阅读
The nonlinear Schr(o)odinger equation (NLS) is a widely applicable model for wave packets dynamics [1].For wave propagation in aninhomogeneous medium, e.g.a fluid with variable depth or an optical fiber with spatially dependent dispersion, variable coefficient NLS equation (VCNLS) or variable coefficient Korteweg-de Vries models [2], are relevant.Here VCNLS with real dispersion in the presence of linear and/or nonlinear gain/loss is solved exactly.A modified Hirota bilinear method which has been used earlier in the literature to treat the complex Ginzburg Landau equation is employed [3].An additional ingredient isthe usage of time-or space-dependent wave numbers [4].One-soliton solution of such VCNLS is obtained in an analytical form.One restriction of the present algorithm is that the coefficient of the second-order dispersion must be real.A simple example of an exponentially modulated dispersion profile is worked out in detail to illustrate the principle.The competition between the linear gain and nonlinear loss, and vice versa, is investigated.The stability of the solitary waves is tested in direct simulations.They appear to be very robust objects.
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