کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4629825 | 1340586 | 2013 | 14 صفحه PDF | دانلود رایگان |
We study the corresponding scattering problem for Zakharov and Shabat compatible differential equations in two-dimensions, the representation for a solution of the nonlinear Schrödinger equation is formulated as a variational problem in two-dimensions. We extend the derivation to the variational principle for the Zakharov and Shabat equations in one-dimension. We also developed an approximate analytical technique for finding discrete eigenvalues of the complex spectral parameters in Zakharov and Shabat equations for a given pulse-shaped potential, which is equivalent to the physically important problem of finding the soliton content of the given initial pulse. Using a trial function in a rectangular box we find the functional integral. The general case for the two box potential can be obtained on the basis of a different ansatz where we approximate the Jost function by polynomials of order nn instead of a piecewise linear function. We also demonstrated that the simplest version of the variational approximation, based on trial functions with one, two and n-free parameters respectively, and treated analytically.
Journal: Applied Mathematics and Computation - Volume 219, Issue 10, 15 January 2013, Pages 5635–5648