scholarly journals The Dirichlet isospectral problem for trapezoids

2021 ◽  
Vol 62 (5) ◽  
pp. 051511
Author(s):  
Hamid Hezari ◽  
Z. Lu ◽  
J. Rowlett
Keyword(s):  
Isospectral Problem

scholarly journals The Neumann Isospectral Problem for Trapezoids

2017 ◽  
Vol 18 (12) ◽  
pp. 3759-3792 ◽  
Author(s):  
Hamid Hezari ◽  
Zhiqin Lu ◽  
Julie Rowlett
Keyword(s):  
Isospectral Problem

The Multi-Component Jaulent-Miodek Hierarchy and its Multi-Component Integrable Coupling System with Two Arbitrary Functions

2012 ◽  
Vol 442 ◽  
pp. 124-128
Author(s):  
Jian Ya Ge ◽  
Tie Cheng Xia
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Loop Algebra ◽  
Simple Loop ◽  
Coupling System ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Integrable Coupling

We devise a new simple loop algebra GM and an isospectral problem. By making use of Tu scheme, the multi-component Jaulent-Miodek (JM) hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM the multi-component integrable couplings system with two arbitrary functions of the multi-component Jaulent-Miodek (JM) hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchies.

scholarly journals Inverse scattering transform for a new non-isospectral integrable non-linear AKNS model

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 153-160 ◽  
Author(s):  
Xudong Gao ◽  
Sheng Zhang
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Inverse Scattering ◽  
Spectral Parameter ◽  
Soliton Solutions ◽  
Transformation Method ◽  
Linear Partial Differential Equations ◽  
Scattering Transform ◽  
Non Linear ◽  
Isospectral Problem

Constructing integrable systems and solving non-linear partial differential equations are important and interesting in non-linear science. In this paper, Ablowitz-Kaup-Newell-Segur (AKNS)?s linear isospectral problem and its accompanied time evolution equation are first generalized by embedding a new non-isospectral parameter whose varying with time obeys an arbitrary smooth enough function of the spectral parameter. Based on the generalized AKNS linear problem and its evolution equation, a new non-isospectral Lax integrable non-linear AKNS model is then derived. Furthermore, exact solutions of the derived AKNS model is obtained by extending the inverse scattering transformation method with new time-varying spectral parameter. In the case of reflectinless potentials, explicit n-soliton solutions are finally formulated through the obtained exact solutions.

SPECTRAL RADIUS ANALYSIS OF MATRICES AND THE ASSOCIATED WITH INTEGRABLE SYSTEMS

2009 ◽  
Vol 23 (24) ◽  
pp. 4855-4879 ◽  
Author(s):  
HONWAH TAM ◽  
YUFENG ZHANG
Keyword(s):  
Lie Algebra ◽  
Spectral Radius ◽  
Integrable Systems ◽  
Hamiltonian Structure ◽  
Soliton Equation ◽  
Spectral Matrix ◽  
Akns Hierarchy ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Set Up

An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

scholarly journals Derivation and soliton dynamics of a new non-isospectral and variable-coefficient system

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 639-646
Author(s):  
Bo Xu ◽  
Sheng Zhang
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Inelastic Collisions ◽  
Time Varying ◽  
Transform Method ◽  
Soliton Dynamics ◽  
Scattering Transform ◽  
Isospectral Problem ◽  
Time Evolution Equation

Under investigation in this paper is a new and more general non-isospectral and variable-coefficient non-linear integrodifferential system. Such a system is Lax integrable because of its derivation from the compatibility condition of a generalized linear non-isospectral problem and its accompanied time evolution equation which is generalized in this paper by embedding four arbitrary smooth enough functions. Soliton solutions of the derived system are obtained in the framework of the inverse scattering transform method with a time-varying spectral parameter. It is graphically shown the dynamical evolutions of the obtained soliton solutions possess time-varying amplitudes and that the inelastic collisions can happen between two-soliton solutions.

scholarly journals On the isospectral problem of the dispersionless Camassa–Holm equation

2013 ◽  
Vol 235 ◽  
pp. 469-495 ◽  
Author(s):  
Jonathan Eckhardt ◽  
Gerald Teschl
Keyword(s):  
Holm Equation ◽  
Isospectral Problem

A GENERALIZED LEVI HIERARCHY AND ITS INTEGRABLE COUPLINGS

2010 ◽  
Vol 24 (17) ◽  
pp. 3453-3460 ◽  
Author(s):  
JIAO ZHANG ◽  
XIAOLI WEI
Keyword(s):  
Integrable Hierarchy ◽  
Integrable Couplings ◽  
Isospectral Problem

In this paper, by making use of the generalized Tu scheme, we consider an isospectral problem, and then a new integrable hierarchy is constructed. It is shown that the generalized Levi hierarchy can be obtained as a reduction. Further, integrable couplings of the generalized Levi hierarchy is produced based on an enlarging isospectral problem.

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