We study quadruple-mode (quadrupole) solitons in nonlocal media with different degrees of nonlocality. The existence and stability of such quadrupole solitons is addressed systematically. The solution of quadrupole solitons is obtained analytically with variational approach. The propagation dynamics of quadrupole solitons is found numerically with the split-step method. The repulsion between the out-of-phase petals of quadrupole solitons can not be balanced by the weak nonlocality, leading to the formation of four separated scalar solitons. Completely stable quadrupole solitons can be achieved when the nonlocality is strong.

中文翻译：

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四极子孤子在非本地介质中的稳定性

我们研究具有不同程度的非局域性的非局域介质中的四模（四极）孤子。这类四极孤子的存在和稳定性得到系统地解决。通过变分方法解析得出四极子孤子的解。四极子孤子的传播动力学可以通过分步法得到。四极子孤子的异相瓣之间的斥力不能通过弱的非局部性来平衡，从而导致形成四个分离的标量孤子。当非局部性较强时，可以实现完全稳定的四极孤子。