We derive the expressions for the collision-induced amplitude dynamics of two flat-top solitons in spatial dimensions of 1, 2, and 3 caused by the generic weak nonlinear loss under the framework of coupled cubic-quintic ($n+1$)D nonlinear Schrödinger equations for $n=1,2,3$. We develop a new perturbative technique which is mainly based on the calculations for the fast collision-induced changes in the soliton envelope and the use of the single perturbed soliton solution for the calculations. These results quantify the energy dropdown due to a fast collision of two pulses ($n=1)$, or two optical beams ($n=2$), or two light bullets ($n=3$) in cubic-quintic nonlinear media with dissipation. The theoretical calculations are then confirmed by numerical simulations with the corresponding coupled nonlinear Schrödinger equations. Our approach can be used for studying the effects of dissipation on colliding solitons described by the coupled nonlinear Schrödinger models, where the unperturbed equation is nonintegrable.

我们推导了在耦合的立方五次方框架下，由一般的弱非线性损耗引起的，在空间维度为1,2和3的两个平顶孤子在碰撞中引起的振幅动力学的表达式。$ñ+\mathrm{1个}$）D非线性Schrödinger方程 $ñ=\mathrm{1个}，\mathrm{2个}，3$。我们开发了一种新的摄动技术，其主要基于对孤子包络线中快速碰撞诱发的变化的计算，以及基于单个摄动孤子解的计算。这些结果量化了由于两个脉冲的快速碰撞而导致的能量下降（$ñ=\mathrm{1个}）$或两个光束（$ñ=\mathrm{2个}$）或两颗子弹（$ñ=3$）在具有耗散的立方五次非线性介质中。然后，通过相应的耦合非线性Schrödinger方程的数值模拟，可以确认理论计算。我们的方法可以用于研究在碰撞由耦合非线性薛定谔模型，其中所描述的孤子耗散的效果未受扰动方程是不可积。