Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates
The any multi-component nonlinear Schrödinger (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...
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| Published in | Journal of nonlinear science Vol. 31; no. 5 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.10.2021
Springer Nature B.V |
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| Abstract | The any multi-component nonlinear Schrödinger (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 multi-component 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. |
|---|---|
| AbstractList | The any multi-component nonlinear Schrödinger (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 Fℓ(z), which pave a powerful way in the study of vector RW structures of the multi-component 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. The any multi-component nonlinear Schrödinger (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 multi-component 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. |
| ArticleNumber | 81 |
| Author | Zhang, Guoqiang Ling, Liming Yan, Zhenya |
| Author_xml | – sequence: 1 givenname: Guoqiang surname: Zhang fullname: Zhang, Guoqiang organization: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences – sequence: 2 givenname: Liming surname: Ling fullname: Ling, Liming organization: School of Mathematics, South China University of Technology – sequence: 3 givenname: Zhenya orcidid: 0000-0002-9475-3753 surname: Yan fullname: Yan, Zhenya email: zyyan@mmrc.iss.ac.cn organization: Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, School of Mathematical Sciences, University of Chinese Academy of Sciences |
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| Keywords | Parity-time-reversal symmetry Multi-component NLS equations Lax pair Loop group method 35Q55 Asymptotic estimates 37K40 35Q51 37K10 Nonzero boundary conditions Darboux transform 35Q15 Governing polynomial Higher-order vector Peregrine solitons |
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| Snippet | The any multi-component nonlinear Schrödinger (alias
n
-NLS) equations with nonzero boundary conditions are studied. We first find the fundamental and... The any multi-component nonlinear Schrödinger (alias n-NLS) equations with nonzero boundary conditions are studied. We first find the fundamental and... |
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| SubjectTerms | Analysis Asymptotic properties Boundary conditions Classical Mechanics Economic Theory/Quantitative Economics/Mathematical Methods Group theory Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Nonlinear systems Parameters Polynomials Schrodinger equation Solitary waves Theoretical |
| Title | Multi-component Nonlinear Schrödinger Equations with Nonzero Boundary Conditions: Higher-Order Vector Peregrine Solitons and Asymptotic Estimates |
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