What is it about?
The NLS equation is a fundamental model in nonlinear physical systems. And we consider the more general form of NLS equation, the n-component NLS equations. The rich interactions between solitons are shown in our work. The law of interactions between solitons are summarized, and then we predict the interactions between any N solitons.
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Photo by Marko Blažević on Unsplash
Why is it important?
The mathematical expressions for the soliton solutions of the n-component NLS equations are very complex and it is very difficult to study the interactions between solitons by means of formulas. Through rich and meaningful images, we have summarised the laws governing the interactions between solitons. These results not only reveal the intrinsic characteristics of solitons, but will also facilitate the application of the NLS equation to physics.
Perspectives
I hope that this article will make more people aware of the beauty of mathematics. Mathematics is more than just tedious derivations and formulas; it is actually rich in substance and laws that can reveal many natural phenomena.
Yuan Li
Fudan University
Read the Original
This page is a summary of: Riemann–Hilbert problem and interactions of solitons in the ‐component nonlinear Schrödinger equations, Studies in Applied Mathematics, September 2021, Wiley,
DOI: 10.1111/sapm.12450.
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