Exact soliton solutions of coupled nonlinear Schrödinger equations: shape-changing collisions, logic gates, and partially coherent solitons.
Exact soliton solutions of coupled nonlinear Schrödinger equations: shape-changing collisions, logic gates, and partially coherent solitons.
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DOI：
10.1103/physreve.67.046617
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
T. Kanna;M. Lakshmanan
中科院分区：
文献类型：
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作者：
T. Kanna;M. Lakshmanan
研究了耦合非线性薛定谔方程组中孤子相互作用的不同动力学特征，该方程组模拟了非线性光学中不同物理条件下多模波的传播。本文通过显式构造多孤子解，本文利用Hirota双线性化方法对两耦合和任意N耦合非线性薛定谔方程组（最多四个孤子解）进行了研究，清楚地揭示了这些奇异形状变化背后的各种特征（强度重新分布）孤子的碰撞，包括振幅、相位和相对分离距离的变化，以及孤子模式之间能量重新分配的许多可能性。然而，在这个多孤子碰撞过程中的成对碰撞的性质被证明是保存尽管孤子的振幅和相位的变化。详细的渐近分析还表明，当孤子发生多次碰撞时，在两个以上的孤子相互作用过程中，存在至少一个孤子形状恢复的可能性，这些孤子的相互作用可以用三阶或更高阶孤子解来表示.从应用的角度来看，我们已经表明，从渐近表达式的振幅（强度）重新分布可以写为一个广义线性分式变换的N分量的情况下。此外，我们指出如何多孤子可以被重新解释为各种逻辑门的孤子参数的适当选择，导致可能的多态逻辑。此外，我们还指出，最近研究的各种部分相干孤子只是发生形变碰撞的亮孤子解的特例，从而解释了它们在碰撞过程中的形状变化和形状变化.
The different dynamical features underlying soliton interactions in coupled nonlinear Schrödinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (up to four-soliton solutions) for two-coupled and arbitrary N-coupled nonlinear Schrödinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However, in this multisoliton collision process the pairwise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of at least one soliton during interactions of more than two solitons represented by three- and higher-order soliton solutions. From an application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the N-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape-changing collisions, thereby explaining their variable profile and shape variation in collision process.