Nonlinear waves and the Inverse Scattering Transform
Nonlinear waves and the Inverse Scattering Transform
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DOI：
10.1016/j.ijleo.2023.170710
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发表时间：
2023-02
期刊：
影响因子：
3.1
通讯作者：
M. Ablowitz
中科院分区：
文献类型：
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作者：
M. Ablowitz
孤子是一类稳定的非线性局域波。它们广泛地出现在物理问题中;应用包括水波、等离子体物理、玻色-爱因斯坦凝聚和非线性光学。这种局部水波可以追溯到19世纪的研究。1973年，长谷川和塔佩特发现了光纤中的亮孤子和暗孤子。在20世纪70年代出现了一个通用理论，它允许人们线性化并明确找到一类非线性波动方程的孤子解，包括物理上重要的方程，如Korteweg-deVries，非线性薛定谔（NLS）和sine-Gordon方程。孤立子连接到基本线性散射方程的本征值/束缚态。由Ablowitz，Kaup，纽韦尔，Segur提出的逆散射变换（IST）理论，可以线性化/求解广泛的非线性波动方程。2013年，该理论被扩展到新的非局部非线性波动方程，包括PT对称和逆时空非线性方程。在2022年，该理论被证明包含分数可积非线性系统;分数KdV和NLS方程是范例。
Solitons are a class of nonlinear stable, localized waves. They arise widely in physical problems; applications include water waves, plasma physics, Bose–Einstein condensation and nonlinear optics. Such localized water waves can be traced back to research in the 1800s. In fiber optics ‘bright and dark’ solitons were discovered in 1973 by Hasegawa and Tappert. In the 1970s a general theory emerged which allows one to linearize and explicitly find soliton solutions to a class of nonlinear wave equations including physically significant equations such as the Korteweg–deVries, nonlinear Schrödinger (NLS) and sine-Gordon equations. Solitons are connected to eigenvalues/bound states of underlying linear scattering equations. The theory, termed the Inverse Scattering Transform (IST) by Ablowitz, Kaup, Newell, Segur, leads to linearization/solutions to broad classes of nonlinear wave equations. In 2013 the theory was extended to novel classes of nonlocal nonlinear wave equations including PT symmetric and reverse-space–time nonlinear equations. In 2022 the theory was shown to encompass fractional integrable nonlinear systems; the fractional KdV and NLS equations are paradigms.