共查询到16条相似文献,搜索用时 78 毫秒
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研究一类广义非线性Schrordinger方程的孤立子解及其性质,研究非线性参数变化时孤立子性态的变化规律,同时研究该系统的数值解法,得到了一类广义非线性Schroedinger方程差分格式的收敛性和稳定性的条件。 相似文献
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The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation 下载免费PDF全文
This paper studies a generalized nonlinear evolution equation. Using
the homotopic mapping method, it constructs a corresponding homotopic
mapping transform. Selecting a suitable initial approximation and
using homotopic mapping, it obtains an approximate solution with an
arbitrary degree of accuracy for the solitary wave. From the
approximate solution obtained by using the homotopic mapping method, it
possesses a good accuracy. 相似文献
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It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well. 相似文献
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Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions. 相似文献
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根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.
关键词:
非线性波方程
尖峰孤子解
待定系数法 相似文献