In this work, the extended Poincaré–Lighthill–Kuo (PLK) technique is devoted to reduce the fluid govern equations of complex plasma species to two coupled evolution equations (including the damping Korteweg–de Vries (dKdV) equation and damping modified Korteweg–de Vries (dmKdV) equation) for studying the dissipative soliton collisions in a collisional complex unmagnetized plasma. To find the phase shifts of both the dKdV and dmKdV solitons after collisions, the solutions of the evolution equations must be determined precisely. For this purpose, the homotopy perturbation method is introduced to find high-accuracy approximate numerical solutions to both the dKdV and dmKdV equations after few iterations (approximations). Moreover, and for the first time, we will find some approximate analytic solutions for the evolution equations in order to investigate the characteristics of the dissipative solitons after collisions. Furthermore, the comparison between the approximate numerical and analytical dissipative solutions of both the dKdV and dmKdV equations will be checked. Thereafter, a set of analytical expressions for the phase shifts of the normal and dissipative soliton collisions will be estimated. The effects of plasma configurational parameters on the phase shifts of colliding solitons will be examined.

在这项工作中，扩展的庞加莱-莱特希尔-库（PLK）技术致力于将复杂等离子体物种的流体控制方程简化为两个耦合的演化方程（包括阻尼Korteweg-de Vries（dKdV）方程和阻尼修正Korteweg-de Vries（dmKdV）方程）用于研究碰撞复合未磁化等离子体中的耗散孤子碰撞。为了找到碰撞后dKdV和dmKdV孤子的相移，必须精确确定演化方程的解。为此，引入了同伦摄动方法，以在几次迭代（逼近）之后找到dKdV和dmKdV方程的高精度近似数值解。而且，这是第一次 我们将找到一些演化方程的近似解析解，以研究碰撞后耗散孤子的特性。此外，将检查dKdV和dmKdV方程的近似数值和解析耗散解之间的比较。此后，将估计正常和耗散孤子碰撞的相移的一组解析表达式。将检查等离子体构型参数对碰撞孤子相移的影响。将估计一组正常和耗散孤子碰撞的相移的解析表达式。将检查等离子体构型参数对碰撞孤子相移的影响。将估计一组正常和耗散孤子碰撞的相移的解析表达式。将检查等离子体构型参数对碰撞孤子相移的影响。