Abstract Head-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

中文翻译：

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多孤子正面碰撞导致带负电等离子体中的孤子湍流

摘要 在两个 Korteweg de Vries (KdV) 方程的框架内，研究了四个尘埃离子声学 (DIA) 孤子的迎面相互作用以及由沿相反方向运动的孤子的迎面相互作用引起的波场的统计特性。应用扩展的 Poincaré-Lighthill-Kuo (PLK) 方法从由麦克斯韦负离子、冷移动正离子、κ 分布电子和带正电荷的尘埃颗粒组成的未磁化四组分等离子体模型中获得两个相反运动的 KdV 方程。采用Hirota双线性方法得到两个KdV方程的双孤子解，由此呈现四个孤子正面碰撞引起的孤子湍流行为。获得最强相互作用点处合成波形的幅度和形状。为了查看正面碰撞对波场统计特性的影响，计算了前四个矩。观察到正面碰撞对第一积分矩没有影响，而在四个孤子的主要相互作用区域中第二、第三和第四力矩增加，这是孤子湍流的明确指示。