Multicomponent Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: HigherOrder Vector Peregrine Solitons and Asymptotic Estimates
Abstract
The any multicomponent nonlinear Schrödinger (alias nNLS) equations with nonzero boundary conditions are studied. We first find the fundamental and higherorder vector Peregrine solitons (alias rational rogue waves (RWs)) for the nNLS equations by using the loop group theory, an explicit (n +1 )multiple root of a characteristic polynomial of degree (n +1 ) related to the BenjaminFeir instability, and inverse functions. Particularly, the fundamental vector rational RWs are proved to be paritytimereversal 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 socalled 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 multicomponent nonlinear physical systems.
 Publication:

Journal of NonLinear Science
 Pub Date:
 October 2021
 DOI:
 10.1007/s0033202109735z
 arXiv:
 arXiv:2012.15603
 Bibcode:
 2021JNS....31...81Z
 Keywords:

 Multicomponent NLS equations;
 Nonzero boundary conditions;
 Lax pair;
 Loop group method;
 Darboux transform;
 Higherorder vector Peregrine solitons;
 Paritytimereversal symmetry;
 Governing polynomial;
 Asymptotic estimates;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Computational Physics
 EPrint:
 42 pages, 7 figures