We show that the generalized nonlinear Schrödinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance between the quartic and quadratic dispersions with the Kerr nonlinearity, and they come in infinite families with different signatures. A traveling wave ansatz, where the optical pulse does not undergo a change in shape while propagating, allows us to transform the GNLSE into a fourth-order nonlinear Hamiltonian ordinary differential equation with two reversibilities. Studying families of connecting orbits with different symmetry properties of this reduced system, connecting equilibria to themselves or to periodic solutions, provides the key to understanding the overall structure of solitons of the GNLSE. Integrating a perturbation of them as solutions of the GNLSE suggests that some of these solitons may be observable experimentally in photonic crystal waveguides over several dispersion lengths.

中文翻译：

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具有四次色散的非线性薛定谔方程中的无限多个不同对称类型的多脉冲孤子

我们表明，具有四次色散的广义非线性薛定谔方程 (GNLSE) 支持无限多的多脉冲孤子，适用于广泛的色散项参数范围。这些孤子通过具有克尔非线性的四次和二次色散之间的平衡而存在，并且它们来自具有不同特征的无限族。行波 ansatz，其中光脉冲在传播时不发生形状变化，允许我们将 GNLSE 转换为具有两个可逆性的四阶非线性哈密顿常微分方程。研究这个简化系统的具有不同对称特性的连接轨道族，将平衡与其自身或周期解连接起来，为理解 GNLSE 孤子的整体结构提供了关键。