Exact solutions in a form of bright solitons are obtained for the nonlinear Schrödinger equations with general quartic or quintic nonlinearities. The solutions, expressed in terms of the elliptic integrals, are implicit. An existence of flat-top solitons is shown, and the corresponding condition is obtained. The stability of solitons is analyzed for different system parameters. Numerical simulations show three different scenarios of the soliton instability, namely the soliton decay, oscillations and collapse.

中文翻译：

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广义非线性薛定ding方程的孤子

对于具有一般四次或五次非线性的非线性Schrödinger方程，可以得到明亮孤子形式的精确解。用椭圆积分表示的解是隐式的。显示了平顶孤子的存在，并获得了相应的条件。针对不同的系统参数分析了孤子的稳定性。数值模拟显示了孤子不稳定性的三种不同情况，即孤子衰减，振荡和坍塌。