We analyze generalized \((3+1)\)-dimensional Yu–Toda–Sasa–Fukuyama(YTSF) equation, a nonlinear evolution equation to understand pulse behavior when variations are strong. Using the Lie symmetry reduction, the generalized form of (3+1)-dimensional YTSF equation is reduced to ordinary differential equations. We introduce the main result for the analysis of soliton solutions that accounts for perturbation and dispersion of the waveform including linear and nonlinear effects. We discuss soliton interactions as a key feature of soliton based telecommunication transmission systems. Solitons propagate at distinct speed and interact quite strongly with each other having beaming correspondence. Though the interaction is transient, the coherence is diagonally placed. The solitons after perfectly elastic collisions recover their shape, amplitude and velocity except phase shift.

中文翻译：

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基于李对称性的广义$$（3 + 1）$$（3 +1）维Yu–Toda–Sasa–Fukuyama方程的孤子解

我们分析广义\（（3 + 1）\）三维Yu–Toda–Sasa–Fukuyama（YTSF）方程，这是一个非线性演化方程，用于理解变化较大时的脉冲行为。使用李对称性约简，将（3 + 1）维YTSF方程的广义形式简化为常微分方程。我们介绍了孤子解决方案分析的主要结果，该结果说明了包括线性和非线性效应在内的波形的摄动和离散。我们讨论孤子相互作用，将其作为基于孤子的电信传输系统的关键特征。孤子以不同的速度传播，并且彼此之间具有强烈的对应关系，并具有令人愉快的交互作用。尽管相互作用是短暂的，但相干关系是对角线放置的。完全弹性碰撞后的孤子会恢复其形状，幅度和速度（相移除外）。