Abundant solutions for the Lakshmanan-Porsezian-Daniel equation in an optical fiber through Riemann-Hilbert approach

被引：5

作者：

Guo, Han-Dong ^{[1
]}

Xia, Tie-Cheng ^{[2
]}

Tong, Li-Ning ^{[2
]}

机构：

[1] Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou 450045, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

MODERN PHYSICS LETTERS B | 2022年 / 36卷 / 21期

基金：

中国国家自然科学基金;

关键词：

Riemann-Hilbert approach; spectral analysis; Lakshmanan-Porsezian-Daniel equation; breathers; solitons; N-SOLITON SOLUTIONS; LONG-TIME ASYMPTOTICS; BRIGHT; INTEGRABILITY;

D O I：

10.1142/S0217984922500580

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

The integrable Lakshmanan-Porsezian-Daniel (LPD) equation originating in nonlinear fiber is studied in this work via the Riemann-Hilbert (RH) approach. First, we give the spectral analysis of the Lax pair, from which an RH problem is formulated. Afterwards, by solving the special RH problem with reflectionless under the conditions of irregularity, the formula of general N-soliton solutions can be obtained. In addition, the localized structures and dynamic behaviors of the breathers and solitons corresponding to the real part, imaginary part and modulus of the resulting solution r(x, t) are shown graphically and discussed in detail. Unlike 1- or 2-order breathers and solitons, 3-order breathers and soliton solutions rapidly collapse when they interact with each other. This phenomenon results in unbounded amplitudes which imply that higher-order solitons are not a simple nonlinear superposition of basic soliton solutions.

引用

页数：14

共 37 条

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