Journal ArticleDOI
Nonlinear continuous integrable Hamiltonian couplings
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TLDR
Based on a kind of special non-semisimple Lie algebras, a scheme is presented for constructing nonlinear continuous integrable couplings of the AKNS hierarchy of soliton equations.About:
This article is published in Applied Mathematics and Computation.The article was published on 2011-05-01. It has received 50 citations till now. The article focuses on the topics: Integrable system & Lie conformal algebra.read more
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Applied Mathematics and Computation
TL;DR: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions by introducing graphs representing the domain of integration of the integrals in each term.
Journal ArticleDOI
Loop algebras and bi-integrable couplings
TL;DR: In this paper, a class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.
Journal ArticleDOI
Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation
TL;DR: In this article, the bilinear form and exact periodic wave solutions of a class of (2 + 1)-dimensional nonlinear integrable differential equations directly and quickly with the help of generalized D-p-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method were obtained.
Journal ArticleDOI
Lie Algebras for Constructing Nonlinear Integrable Couplings
TL;DR: In this article, two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ) hierarchy and the Yang hierarchy are obtained.
Journal ArticleDOI
An integrable system and associated integrable models as well as Hamiltonian structures
Hon Wah Tam,Yufeng Zhang +1 more
TL;DR: In this paper, a Lie algebra A1 = {e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15, e16, e17, e18, e19, e20, e21, e22, e23] is used to generate eight higher-dimensional Lie algebras from which the linear integrable couplings, the nonlinear integrably couplings and the bi-
References
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Journal ArticleDOI
The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Journal ArticleDOI
A Simple model of the integrable Hamiltonian equation
TL;DR: In this paper, a method of analysis of the infinite-dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested, based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equation with their symmetries by using symplectic operators.
Journal ArticleDOI
A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
Applied Mathematics and Computation
TL;DR: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions by introducing graphs representing the domain of integration of the integrals in each term.
Journal ArticleDOI
Integrable theory of the perturbation equations
Wen-Xiu Ma,Benno Fuchssteiner +1 more
TL;DR: In this paper, an integrable theory for perturbation equations engendered from small disturbances of solutions is developed, which includes various integrability properties of the perturbations, such as hereditary recursion operators, master symmetries, linear representations (Lax and zero curvature representations) and Hamiltonian structures, and provides us with a method of generating hereditary operators, Hamiltonian operators and symplectic operators starting from the known ones.
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