التفاصيل البيبلوغرافية
| العنوان: |
Differential Relations for the Solutions to the NLS Equation and Their Different Representations |
| المؤلفون: |
Pierre Gaillard |
| المصدر: |
Communications in Advanced Mathematical Sciences, Vol 2, Iss 4, Pp 235-243 (2019) |
| بيانات النشر: |
Emrah Evren KARA, 2019. |
| سنة النشر: |
2019 |
| المجموعة: |
LCC:Mathematics |
| مصطلحات موضوعية: |
nls equation, fredholm determinants, peregrine breathers, rogue waves, wronskians, Mathematics, QA1-939 |
| الوصف: |
Solutions to the focusing nonlinear Schr\"odinger equation (NLS) of order $N$ depending on $2N-2$ real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasi-rational solutions to the NLS equation denoted by $v_{N}$ and have been explicitly constructed until order $N = 13$. These solutions appear as deformations of the Peregrine breather $P_{N}$ as they can be obtained when all parameters are equal to $0$. These quasi rational solutions can be expressed as a quotient of two polynomials of degree $N(N+1)$ in the variables $x$ and $t$ and the maximum of the modulus of the Peregrine breather of order $N$ is equal to $2N+1$. \\ Here we give some relations between solutions to this equation. In particular, we present a connection between the modulus of these solutions and the denominator part of their rational expressions. Some relations between numerator and denominator of the Peregrine breather are presented. |
| نوع الوثيقة: |
article |
| وصف الملف: |
electronic resource |
| اللغة: |
English |
| تدمد: |
2651-4001 |
| Relation: |
https://dergipark.org.tr/tr/download/article-file/755522; https://doaj.org/toc/2651-4001 |
| DOI: |
10.33434/cams.558044 |
| URL الوصول: |
https://doaj.org/article/8addbe2d8d7e464395962768b803599e |
| رقم الانضمام: |
edsdoj.8addbe2d8d7e464395962768b803599e |
| قاعدة البيانات: |
Directory of Open Access Journals |