A Nonlinear Difference Scheme and Inverse Scattering
A Nonlinear Difference Scheme and Inverse Scattering
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DOI：
10.1002/sapm1976553213
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发表时间：
1976-09
影响因子：
2.7
通讯作者：
M. Ablowitz;J. Ladik
中科院分区：
文献类型：
--
作者：
M. Ablowitz;J. Ladik
得到了一个非线性偏差分方程，并用逆散射法求解。在一定的连续统极限下，证明了该方程如何近似于非线性薛定谔方程和相关的非线性微分差分方程。在任何时候解都可以比较，并证明该方案是收敛的。这些思想也适用于其他非线性演化方程。
A nonlinear partial difference equation is obtained and solved by the method of inverse scattering. In a certain continuum limit it is shown how this equation approximates the nonlinear Schrodinger equation and a related nonlinear differential‐difference equation. At all times the solutions can be compared, and the scheme is shown to be convergent. These ideas apply to other nonlinear evolution equations as well.