Multi-component Nonlinear Schrodinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates

作者：Zhang, Guoqiang; Ling, Liming; Yan, Zhenya^*

来源：Journal of Nonlinear Science, 2021, 31(5): 81.

DOI：10.1007/s00332-021-09735-z

• Multi-component NLS equations
• Nonzero boundary conditions
• Lax pair
• Loop group method
• Darboux transform
• Higher-order vector Peregrine solitons
• Parity-time-reversal symmetry
• Governing polynomial
• Asymptotic estimates

The any multi-component nonlinear Schrodinger (alias n-NLS) equations with nonzero boundary conditions are studied. We first find the fundamental and higher-order vector Peregrine solitons (alias rational rogue waves (RWs)) for the n-NLS equations by using the loop group theory, an explicit (n + 1)-multiple root of a characteristic polynomial of degree (n + 1) related to the Benjamin-Feir instability, and inverse functions. Particularly, the fundamental vector rational RWs are proved to be parity-time-reversal symmetric for some parameter constraints and classified into n cases in terms of the degree of the introduced polynomial. Moreover, a systematic approach is proposed to study the asymptotic behaviors of these vector RWs such that the decompositions of RWs are related to the so-called governing polynomials F-l(z), which pave a powerful way in the study of vector RW structures of the multicomponent integrable systems. The vector RWs with maximal amplitudes can also be determined via the parameter vectors, which are interesting and useful in the study of RWs for multi-component nonlinear physical systems.

• 单位
  中国科学院; 中国科学院研究生院