Journal ArticleDOI
Generalized fractional supertrace identity for Hamiltonian structure of NLS–MKdV hierarchy with self-consistent sources
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TLDR
Based on the modified Riemann-Liouville fractional derivative and Tu scheme, the fractional super NLS-MKdV hierarchy is derived, especially the self-consistent sources term is considered as discussed by the authors.Abstract:
In the paper, based on the modified Riemann–Liouville fractional derivative and Tu scheme, the fractional super NLS–MKdV hierarchy is derived, especially the self-consistent sources term is considered. Meanwhile, the generalized fractional supertrace identity is proposed, which is a beneficial supplement to the existing literature on integrable system. As an application, the super Hamiltonian structure of fractional super NLS–MKdV hierarchy is obtained.read more
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Journal ArticleDOI
Riemann–Hilbert problems and N-soliton solutions for a coupled mKdV system
Wen-Xiu Ma,Wen-Xiu Ma,Wen-Xiu Ma +2 more
TL;DR: In this paper, a 3 × ǫ 3 matrix spectral problem is introduced and its associated AKNS integrable hierarchy with four components is generated from this spectral problem, a kind of Riemann-Hilbert problems is formulated for a system of coupled mKdV equations in the resulting AKNS integral hierarchy.
Journal ArticleDOI
Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions
TL;DR: The fractional order model can open up a new window for better understanding the waves in fluid and help comprehending generalization and evolution of Rossby solitary waves in stratified fluid.
Journal ArticleDOI
Application of the Riemann–Hilbert approach to the multicomponent AKNS integrable hierarchies
TL;DR: In this article, a class of Riemann-Hilbert problems on the real axis is formulated for solving the multicomponent AKNS integrable hierarchies associated with a kind of bock matrix spectral problems.
Journal ArticleDOI
Long-Time Asymptotics of a Three-Component Coupled mKdV System
TL;DR: In this paper, the authors presented an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem.
Journal ArticleDOI
A new ZK–BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property
TL;DR: In this article, a new ZK-BO equation for three-dimensional algebraic Rossby solitary waves is derived by employing perturbation expansions and stretching transformations of time and space.
References
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Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Journal ArticleDOI
The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
TL;DR: In this article, a trace identity based approach to Hamiltonian structures of integrable systems is proposed by making use of trace identity for a variety of isospectral problems that can be unified to one model ψx=Uψ.
Journal ArticleDOI
Mathematics of dispersive water waves
TL;DR: In this article, a commuting hierarchy of dispersive water wave equations makes a three-Hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed.
Journal ArticleDOI
A trace identity and its applications to the theory of discrete integrable systems
TL;DR: In this paper, a general theory for studying discrete integrable systems is developed based on a trace identity that the author previously proposed, and a scheme for generating hierarchies of discrete Integrable Systems is presented.
Journal ArticleDOI
Integration of the soliton hierarchy with self-consistent sources
TL;DR: In this paper, the singularity of the eigenfunctions in the Lax representation of soliton equation with self-consistent sources (SESCS) is treated to determine the evolution of scattering data.
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