The ion-acoustic Gardner solitons in negative ion plasma have been studied. The Gardner equation is deduced by employing the reductive perturbation technique. We have investigated the ion-acoustic Gardner solitons in negative ion plasma in the parametric regime where the KdV equation is no longer valid to study soliton solution. It is found that for a given set of parameter values with negative ion concentration ($\alpha$) less than the critical value (${\alpha }_c$), i.e. $\alpha$<${\alpha }_c$; the system supports compressive Gardner soliton, whereas for $\alpha$>${\alpha }_c,$ rarefactive Gardner soliton exists. It is also investigated that Gardner solitons exist only for the fast mode, whereas no such structure is found in the case of the slow mode. The present study may be helpful to understand the nonlinear ion-acoustic solitary waves in space plasma and laboratory experiment plasmas also can be helpful for the study of Ionospheric auroral and magnetospheric plasmas where negative ions are present.

研究了负离子等离子体中的离子声加德纳孤子。Gardner 方程是通过使用还原微扰技术推导出来的。我们已经在参数化状态下研究了负离子等离子体中的离子声加德纳孤子，其中 KdV 方程不再适用于研究孤子解。发现对于给定的一组具有负离子浓度的参数值（$\alpha$) 小于临界值 (${\alpha }_C$）， IE $\alpha$<${\alpha }_C$; 该系统支持压缩加德纳孤子，而对于$\alpha$>${\alpha }_C,$存在稀有加德纳孤子。还研究了 Gardner 孤子仅存在于快模中，而在慢模的情况下没有发现这种结构。本研究可能有助于了解空间等离子体和实验室实验等离子体中的非线性离子声孤立波，也有助于研究存在负离子的电离层极光和磁层等离子体。