☆ 4.6 Article

Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation

PHYSICA D-NONLINEAR PHENOMENA (2024)

Related references

Note: Only part of the references are listed.

Article Mathematics, Applied

Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy

Minghe Zhang et al.

Summary: This paper investigates the anomalous dispersive relations, inverse scattering transform, and fractional multi-solitons of the integrable combined fractional higher-order mKdV hierarchy. It explores the completeness of squared scalar eigenfunctions and constructs a matrix RH problem to represent three types of fractional N-solitons. The obtained results demonstrate anomalous dispersion and various interesting wave phenomena in fractional nonlinear media.

PHYSICA D-NONLINEAR PHENOMENA (2023)

Add to Collection

Article Physics, Multidisciplinary

Nondegenerate solitons in the integrable fractional coupled Hirota equation

Ling An et al.

Summary: In this paper, we investigate the fractional coupled Hirota equation based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr using the Riesz fractional derivative. Unlike previous nonlinear fractional equations, this type of equation is integrable. By employing the inverse scattering transformation in the reflectionless case, we obtain the fractional n-soliton solutions of the equation. Specifically, we analyze the one-and two-soliton solutions and prove the linear superposition property of the fractional two-soliton as iti -oo. Additionally, we obtain nondegenerate fractional soliton solutions and provide a simple analysis of them.

PHYSICS LETTERS A (2023)

Add to Collection

Article Physics, Multidisciplinary

Fractional Integrable Nonlinear Soliton Equations

Mark J. Ablowitz et al.

Summary: This article presents a new class of integrable fractional nonlinear evolution equations that describe dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process and have been applied to fractional extensions of the Korteweg-deVries and nonlinear Schrodinger equations.

PHYSICAL REVIEW LETTERS (2022)

Add to Collection

Article Physics, Multidisciplinary

Integrable fractional modified Korteweg-deVries, sine-Gordon, and sinh-Gordon equations

Mark J. Ablowitz et al.

Summary: The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations, and can be extended to fractional nonlinear evolution equations characterized by anomalous dispersion. Using symmetries present in the linear scattering problem, these equations can be connected with a scalar family of nonlinear evolution equations, of which fractional mKdV, fsineG, and fsinhG are special cases.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

Add to Collection

Article Mathematics, Interdisciplinary Applications

New integrable multi-Levy-index and mixed fractional nonlinear soliton hierarchies

Zhenya Yan

Summary: This letter presents a simple and new idea to generate two types of novel integrable multi-Levyindex and mix-Levy-index fractional nonlinear soliton hierarchies. Their explicit forms, anomalous dispersion relations, and fractional multi-soliton solutions are obtained in this study.

CHAOS SOLITONS & FRACTALS (2022)

Add to Collection

Article Physics, Multidisciplinary

Fractional integrable and related discrete nonlinear Schrodinger equations

Mark J. Ablowitz et al.

Summary: In this manuscript, a new fractional integrable discrete nonlinear Schrodinger equation is discovered and linearized. Special soliton solutions are found and compared with the closely related fractional averaged discrete nonlinear Schrodinger equation, showing similar behavior for positive fractional parameter and small amplitude waves.

PHYSICS LETTERS A (2022)

Add to Collection

Article Mathematics, Applied

Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrodinger equations

Weifang Weng et al.

Summary: In this paper, the authors used the algorithm by Ablowitz et al. to investigate the integrable fractional higher-order nonlinear Schrodinger equations and found the fractional N-soliton solutions. The analysis of fractional one-, two-, and three-soliton solutions revealed the relationship between their wave, group, and phase velocities and the power laws of their amplitudes. The obtained fractional N-soliton solutions may help explain the super-dispersion transports of nonlinear waves in fractional nonlinear media.

CHAOS (2022)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator

Ming Zhong et al.

Summary: In this paper, the Fourier neural operator (FNO) is extended to discover the mapping between two infinite-dimensional function spaces, and applied to the soliton solutions of fractional integrable nonlinear wave equations. The FNO exhibits powerful approximation capability and the performance is influenced by certain factors.

CHAOS SOLITONS & FRACTALS (2022)

Add to Collection

Article Mathematics, Applied

Darboux transformations and solutions of nonlocal Hirota and Maxwell-Bloch equations

Ling An et al.

Summary: This paper introduces two new types of nonlocal Hirota and Maxwell-Bloch (NH-MB) systems, namely, the PT-symmetric NH-MB system and the reverse space-time NH-MB system, based on the original H-MB system. Darboux transformations were then constructed for these NH-MB systems, leading to explicit solutions being derived.

STUDIES IN APPLIED MATHEMATICS (2021)

Add to Collection

Article Multidisciplinary Sciences

Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies

Liming Ling et al.

Summary: This paper investigates the soliton solutions of nonlocal complex reverse-spacetime mKdV hierarchies through nonlocal symmetry reductions of matrix spectral problems. By formulating the corresponding inverse scattering problems and constructing solutions to specific Riemann-Hilbert problems, N-soliton solutions to the hierarchies are obtained.

SYMMETRY-BASEL (2021)

Add to Collection

Article Optics

Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schrodinger equation with a PT-symmetric potential

Pengfei Li et al.

Summary: The study investigates symmetry-breaking and restoring bifurcations of solitons in a fractional Schrodinger equation, especially in the presence of CQ nonlinearity and a parity-time-symmetric potential. Solitons destabilize at the bifurcation point, but stability is restored through an inverse bifurcation in the case of CQ nonlinearity. Two mutually conjugate branches of ghost states are created in the presence of fractional diffraction.

OPTICS LETTERS (2021)

Add to Collection

Review Computer Science, Interdisciplinary Applications

What is the fractional Laplacian? A comparative review with new results

Anna Lischke et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2020)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Vortex solitons in fractional nonlinear Schrodinger equation with the cubic-quintic nonlinearity

Pengfei Li et al.

CHAOS SOLITONS & FRACTALS (2020)

Add to Collection

Article Mathematics, Applied

The Derivative Nonlinear Schrodinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms andN-Double-Pole Solutions

Guoqiang Zhang et al.

JOURNAL OF NONLINEAR SCIENCE (2020)

Add to Collection

Article Mathematics, Applied

Exact solutions of nonlocal Fokas-Lenells equation

Qinyu Zhang et al.

APPLIED MATHEMATICS LETTERS (2019)

Add to Collection

Article Mathematics

Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method

Dmitry E. Pelinovsky et al.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2018)

Add to Collection

Article Mathematics, Applied

Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrodinger equation

Zi-Xiang Zhou

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2018)

Add to Collection

Article Physics, Fluids & Plasmas

Physically significant nonlocal nonlinear Schrodinger equation and its soliton solutions

Jianke Yang

PHYSICAL REVIEW E (2018)

Add to Collection

Article Mathematics, Applied

Integrable Nonlocal Nonlinear Equations

Mark J. Ablowitz et al.

STUDIES IN APPLIED MATHEMATICS (2017)

Add to Collection

Article Physics, Multidisciplinary

A new fractional operator of variable order: Application in the description of anomalous diffusion

Xiao-Jun Yang et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2017)

Add to Collection

Article Physics, Multidisciplinary

Nonstandard bilinearization of PT-invariant nonlocal nonlinear Schrodinger equation: Bright soliton solutions

S. Stalin et al.

PHYSICS LETTERS A (2017)

Add to Collection

Article Physics, Mathematical

Inverse scattering transform for the focusing nonlinear Schrodinger equation with nonzero boundary conditions

Gino Biondini et al.

JOURNAL OF MATHEMATICAL PHYSICS (2014)

Add to Collection

Article Mathematics, Applied

High-Order Solutions and Generalized Darboux Transformations of Derivative Nonlinear Schrodinger Equations

Boling Guo et al.

STUDIES IN APPLIED MATHEMATICS (2013)

Add to Collection

Article Physics, Multidisciplinary

The Darboux transformation of the derivative nonlinear Schrodinger equation

Shuwei Xu et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2011)

Add to Collection

Article Physics, Multidisciplinary

Fractional variational calculus in terms of Riesz fractional derivatives

O. P. Agrawal

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2007)

Add to Collection

Article Physics, Multidisciplinary

Integrable systems of derivative nonlinear Schrodinger type and their multi-Hamiltonian structure

E Fan

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2001)

Add to Collection

© Peeref 2019-2024. All rights reserved.