非线性薛定谔方程中与Adler-Moser多项式相关的怪波模式
Rogue wave patterns associated with Adler-Moser polynomials in the nonlinear Schrödinger equation
AI总结：
本研究报道了非线性薛定谔方程中由Peregrine波构成的心形、扇形等新怪波模式，证明其渐近由Adler-Moser多项式根结构描述，且比先前模式更多样，解析预测与真实解吻合良好。
摘要：
我们报告了非线性薛定谔方程中新的怪波模式。这些模式包括心形结构、扇形扇区以及许多其他形状，它们由单个Peregrine波组成。当怪波解中的多个内部参数变大时，这些模式就会出现。在解析上，我们证明这些新模式通过膨胀由Adler-Moser多项式的根结构渐近描述。由于Adler-Moser多项式是Yablonskii-Vorob'ev多项式层次的推广，并包含自由复参数，这些与Adler-Moser多项式相关的新怪波模式比先前与Yablonskii-Vorob'ev多项式层次相关的怪波模式更加多样化。我们还将这些模式的解析预测与真实解进行了比较，并展示了它们之间的良好一致性。
英文摘要：
We report new rogue wave patterns in the nonlinear Schrödinger equation. These patterns include heart-shaped structures, fan-shaped sectors, and many others, that are formed by individual Peregrine waves. They appear when multiple internal parameters in the rogue wave solutions get large. Analytically, we show that these new patterns are described asymptotically by root structures of Adler-Moser polynomials through a dilation. Since Adler-Moser polynomials are generalizations of the Yablonskii-Vorob'ev polynomial hierarchy and contain free complex parameters, these new rogue patterns associated with Adler-Moser polynomials are much more diverse than previous rogue patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy. We also compare analytical predictions of these patterns to true solutions and demonstrate good agreement between them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
