【摘 要】
：
We use the inverse scattering method to derive classes of solutions of the system my + |u|2 =0, iut + uxx + 2umx =0 (1)that satisfy the boundary conditions
【机 构】
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Facultad de Ciencias (Matemáticas),Universidad de Salamanca Plaza Merced s/n,E-37008,Salamanca,Spain
【出 处】
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International Conference Nonlinear Waves-Theory and Applicat
论文部分内容阅读
We use the inverse scattering method to derive classes of solutions of the system my + |u|2 =0, iut + uxx + 2umx =0 (1)that satisfy the boundary conditions lim r→∞ |u|(x,y)=1, lim r→∞ ux/u=0, m(x,y=0,t)=0 (2)where r2 ≡ x2 + y2 and u =u(x, y, t).This system is interesting since reduction to the manifold x =y yields the Nonlinear Schr(o)dinger equation (NLS) whereby Eq.(1) generalizes in a natural way NLS to 2+1 dimensions.Under different boundary conditions this equation was proposed first by Shu]man [4] and embedded by Fokas [3] into a general class of integrable equations.See also [2] regarding the radiation spectrum.
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