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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Variational method for the derivative nonlinear Schrodinger equation with computational applications
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Variational method for the derivative nonlinear Schrodinger equation with computational applications

机译：导数非线性薛定inger方程的变分方法及计算应用

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The derivative nonlinear Schrodinger equation (DNLSE) arises as a physical model for ultra-short pulse propagation. In this paper, the existence of a Lagrangian and the invariant variational principle (i.e. in the sense of the inverse problem of calculus of variations through deriving the functional integral corresponding to a given coupled nonlinear partial differential equations) for two-coupled equations describing the nonlinear evolution of the Alfven wave with magnetosonic waves at a much larger scale are given and the functional integral corresponding to those equations is derived. We found the solutions of DNLSE by choice of a trial function in a region of a rectangular box in two cases, and using this trial function, we find the functional integral and the Lagrangian of the system without loss. Solution of the general case for the two-box potential can be obtained on the basis of a different ansatz where we approximate the Jost function using polynomials of order n instead of the piecewise linear function. An example for the third order is given for illustrating the general case.
机译：导数非线性Schrodinger方程（DNLSE）作为超短脉冲传播的物理模型出现。在本文中，存在一个拉格朗日方程和不变变分原理（即，通过推导对应于给定耦合非线性偏微分方程的函数积分的变化演算的反问题）来描述非线性方程组给出了Alfven波随磁声波在更大范围内的演化，并推导了与这些方程相对应的函数积分。我们通过在两种情况下选择矩形框区域中的试验函数找到了DNLSE的解决方案，并使用该试验函数，我们找到了系统的函数积分和Lagrangian且无损失。可以基于不同的ansatz获得两箱电位的一般情况的解，在该ansatz中，我们使用n阶多项式而不是分段线性函数来近似Jost函数。给出了用于说明一般情况的三阶示例。

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