4.7 Article

Lie symmetry analysis, exact solutions, and conservation laws to multi-component nonlinear Schrodinger equations

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Acoustics

Multi-component AKNS systems

Metin Gurses et al.

Summary: We study two members of the multi-component AKNS hierarchy, namely the multi-NLS and multi-MKdV systems. The Hirota bilinear forms of these equations are derived, and soliton solutions are obtained. All possible local and nonlocal reductions of these systems of equations are found, and a prescription is given to obtain their soliton solutions. (2 + 1)-dimensional extensions of the multi-component AKNS systems are also derived.

WAVE MOTION (2023)

Article Mathematics, Applied

Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution

Subhankar Sil et al.

Summary: In this article, we construct exact solutions to a quasilinear system of hyperbolic partial differential equations governing the dynamics of a thin film of a perfectly soluble anti-surfactant solution. Symmetry analysis is performed and various types of symmetries and conserved quantities are computed. The physical interpretation of the obtained solutions, including soliton type solutions, is analyzed. Furthermore, the evolutionary properties of characteristic shock, weak discontinuity, and collision between them are studied using one of the obtained solutions.

APPLIED MATHEMATICS AND COMPUTATION (2023)

Article Engineering, Mechanical

Shape-morphing reduced-order models for nonlinear Schrodinger equations

William Anderson et al.

Summary: This study investigates the reduced-order modeling of nonlinear dispersive waves described by nonlinear Schrodinger (NLS) equations. Two nonlinear reduced-order modeling methods are compared: the reduced Lagrangian approach based on the variational formulation of NLS, and the recently developed method of reduced-order nonlinear solutions (RONS). The surprising result is that, despite their apparent differences, these two methods can be obtained from the real and imaginary parts of a single complex-valued master equation. The study also reveals that the reduced Lagrangian method fails to predict the correct group velocity of waves in the NLS equation, while RONS accurately predicts the correct group velocity.

NONLINEAR DYNAMICS (2022)

Article Engineering, Mechanical

Inverse scattering and soliton solutions of high-order matrix nonlinear Schrodinger equation

Yong Chen et al.

Summary: This study investigates the Riemann-Hilbert problem and soliton solutions to the high-order nonlinear Schrodinger equation with a matrix version through an equivalent spectral problem. By utilizing inverse scattering, a pair of Jost solutions satisfying the asymptotic conditions and the matrix spectral problem are obtained, leading to the matrix Riemann-Hilbert problem. Different soliton solutions are theoretically and graphically presented based on the two types of zero structures of det(P+) in the case of reflection-less.

NONLINEAR DYNAMICS (2022)

Article Mathematics, Applied

Rogue wave patterns in the nonlinear Schrodinger equation

Bo Yang et al.

Summary: The study of rogue wave patterns in the nonlinear Schrodinger equation reveals that these waves exhibit clear geometric structures, formed by Peregrine waves in various shapes with a possible lower-order rogue wave at the center, when an internal parameter is large. These rogue patterns are determined by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy, and their orientations are controlled by the phase of the large parameter. Furthermore, similar rogue patterns can still hold when multiple internal parameters in the rogue waves are large but satisfy certain constraints, with excellent agreement between true rogue patterns and analytical predictions.

PHYSICA D-NONLINEAR PHENOMENA (2021)

Article Mathematics, Applied

A binary Darboux transformation for multicomponent NLS equations and their reductions

Wen-Xiu Ma et al.

Summary: The translation presents a binary Darboux transformation method for multicomponent NLS equations and their reduced integrable counterparts, using pairs of eigenfunctions and adjoint eigenfunctions to generate soliton solutions from a zero potential seed solution.

ANALYSIS AND MATHEMATICAL PHYSICS (2021)

Article Engineering, Mechanical

Lie symmetries, exact solutions and conservation laws of the Date-Jimbo-Kashiwara-Miwa equation

Dig Vijay Tanwar et al.

Summary: This study conducts symmetry reductions and exact solutions of the Date-Jimbo-Kashiwara-Miwa equation using Lie point symmetries, resulting in more generalized solutions and establishing self-adjoint equations and conserved vectors. Numerical simulations are conducted to validate the solutions with physical phenomena.

NONLINEAR DYNAMICS (2021)

Article Mathematics, Applied

A Riemann-Hilbert approach to the Kundu-nonlinear Schr?dinger equation and its multi-component generalization

Jian Li et al.

Summary: This paper focused on studying the N-soliton solutions for the Kundu nonlinear Schrodinger equation. By constructing the matrix Riemann-Hilbert problem and analyzing the spectral problem of the Lax pair, explicit N-soliton solutions for this system were obtained. Additionally, the multi-component Kundu-nonlinear Schrodinger system was generalized and its N-soliton solutions were simplified.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

Article Engineering, Mechanical

Nth-order rogue wave solutions of multicomponent nonlinear Schrodinger equations

Yu-Shan Bai et al.

Summary: This paper constructs a generalized Darboux transformation for multicomponent nonlinear Schrodinger equations, resulting in N th-order rogue wave solutions. Two illustrative examples of three-component and six-component NLS equations are provided, showcasing various solutions including rogue wave solutions and interaction solutions.

NONLINEAR DYNAMICS (2021)

Article Physics, Multidisciplinary

Determining lump solutions for a combined soliton equation in (2+1)-dimensions

Jin-Yun Yang et al.

EUROPEAN PHYSICAL JOURNAL PLUS (2020)

Article Mathematics, Applied

How symmetries yield non-invertible mappings of linear partial differential equations

George W. Bluman et al.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2020)

Article Multidisciplinary Sciences

A third-order nonlinear Schrodinger equation: the exact solutions, group-invariant solutions and conservation laws

Yesim Saglam Ozkan et al.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE (2020)

Article Mathematics

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

Wen-Xiu Ma et al.

JOURNAL OF DIFFERENTIAL EQUATIONS (2018)

Article Engineering, Mechanical

Symmetry analysis and conservation laws to the space-fractional Prandtl equation

Mingyang Pan et al.

NONLINEAR DYNAMICS (2017)

Article Mathematics, Applied

Surfaces and curves corresponding to the solutions generated from periodic seed of NLS equation

Ling Zhang et al.

ACTA MATHEMATICA SINICA-ENGLISH SERIES (2012)

Article Engineering, Mechanical

Approximate conservation laws of perturbed partial differential equations

Yani Gan et al.

NONLINEAR DYNAMICS (2010)

Article Mechanics

Oceanic Rogue Waves

Kristian Dysthe et al.

Annual Review of Fluid Mechanics (2008)

Article Engineering, Mechanical

Governing equations of envelopes created by nearly bichromatic waves on deep water

Ben T. Nohara

NONLINEAR DYNAMICS (2007)

Article Mathematics, Applied

A new conservation theorem

Nail H. Ibragimov

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2007)

Article Mathematics

Spectral analysis of Darboux transformations for the focusing NLS hierarchy

RC Cascaval et al.

JOURNAL D ANALYSE MATHEMATIQUE (2004)