共查询到20条相似文献,搜索用时 24 毫秒
1.
This paper is concerned with the generalized nonlinear second-order equation. By the direct construction method, all of the first-order multipliers of the equation are obtained, and the corresponding complete conservation laws (CLs) of such equations are provided. Furthermore, the integrability of the equation is considered in terms of the conservation laws. In addition, the relationship of multipliers and symmetries of the equations is investigated. 相似文献
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We present an integrable sl(2)-matrix Camassa-Holm(CH) equation.The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws.This equation includes two undetermined functions,which satisfy a system of constraint conditions and may be reduced to a lot of known multicomponent peakon equations.We find a method to construct constraint condition and thus obtain many novel matrix CH equations.For the trivial reduction matrix CH equation we construct its N-peakon solutions. 相似文献
4.
Stephen C. Anco Shahid Mohammad Thomas Wolf Chunrong Zhu 《Journal of Nonlinear Mathematical Physics》2016,23(4):573-606
A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt. 相似文献
5.
S. I. Svinolupov 《Communications in Mathematical Physics》1992,143(3):559-575
The criteria of integrability for the nonlinear Schrödinger-type systems are obtained. One-to-one correspondence between such integrable systems and the Jordan paris is established. It turns out that irreducible systems correspond to simple Jordan pairs. An infinite series of generalized symmetries and local conservation laws for such systems are completely described. 相似文献
6.
QU ChangZheng 《理论物理通讯》2000,33(3):383-388
Generalized Lie symmetries and the integrability of generalized Emden-Fowler equations (GEFEs) are considered. It is shown that the constraint which the variable-coefficient functions must satisfy for the GEFEs to have infinite-dimensional symmetry algebras is precisely the same as this in order that the equation may be transformed into the integrable Emden-Fowler equation. fiom the nature of the symmetry vector fields one can write down the integrals of motion for the above systems. The structure of the symmetry algebras is also presented. 相似文献
7.
N. V. Ustinov 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(3):311-317
The hierarchy of integrable nonlinear equations associated with the quadratic
bundle is considered.
The expressions for the solution of linearization of these equations and
their conservation law in the terms of solutions of corresponding Lax pairs
are found.
It is shown for the first member of the hierarchy that the conservation law is
connected with the solution of linearized equation due to the Noether's
theorem.
The local hierarchy and three nonlocal ones of the infinitesimal symmetries
and conservation laws explicitly expressed through the variables of the
nonlinear equations are derived. 相似文献
8.
The complete lists of vector hyperbolic equations on the sphere that have integrable third-order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability, we mean the existence of vector Bäcklund transformations depending on a parameter. For all new equations, such transformations are constructed. 相似文献
9.
Sequences of canonical conservation laws and generalized symmetries for the lattice Boussinesq and the lattice modified Boussinesq systems are successively derived. The interpretation of these symmetries as differential-difference equations leads to corresponding hierarchies of such equations for which conservation laws and Lax pairs are constructed. Finally, using the continuous symmetry reduction approach, an integrable, multidimensionally consistent system of partial differential equations is derived in relation with the lattice modified Boussinesq system. 相似文献
10.
《Physics letters. A》2020,384(23):126529
In this work, we mainly address two new integrable (2+1)- and (3+1)-dimensional sinh-Gordon equations, which naturally appear in surface theory and fluid dynamics. The first equation includes constant coefficients, while the other is characterized with time-dependent coefficients. It is of further value to investigate the integrability of each model. This study puts forward a Painlevé test to reveal the Painlevé integrability. We show that the first equation passes the Painlevé test to confirm its integrability. However, the compatibility conditions of the second model with time-dependent coefficients provides the relation between these coefficients to ensure its integrability. We show that the dispersion relations of the two equations are distinct, whereas the phase shifts are identical. We apply the simplified Hirota's method where four sets of multiple soliton are derived for these equations. 相似文献
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We study the simple-looking scalar integrable equation fxxt 3( fx ft 1) = 0, which is related (in different ways) to the Novikov, Hirota-Satsuma and Sawada-Kotera equations. For this equation we present a Lax pair, a Bäcklund transformation, soliton and merging soliton solutions (some exhibiting instabilities), two infinite hierarchies of conservation laws, an infinite hierarchy of continuous symmetries, a Painlevé series, a scaling reduction to a third order ODE and its Painlevé series, and the Hirota form (giving further multisoliton solutions). 相似文献
13.
In this paper, by using the classical Lie symmetry approach, Lie point symmetries and reductions of one Blaszak– Marciniak(BM) four-field lattice equation are obtained. Two kinds of exact solutions of a rational form and an exponential form are given. Moreover, we show that the equation has a sequence of generalized symmetries and conservation laws of polynomial form, which further confirms the integrability of the BM system. 相似文献
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We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations. 相似文献
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We study symmetries and conservation laws for Plebañski’s second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems. 相似文献
16.
In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented and analysed. Using the Lie point symmetries, it is showed how to reduce Gordon-type wave equations using the method of invariants, and to obtain exact solutions corresponding to some boundary values. The Noether point symmetries and conservation laws are obtained for the Klein–Gordon equation in one case. Finally, the existence of higherorder variational symmetries of a projection of the Klein–Gordon equation is investigated using the multiplier approach. 相似文献
17.
In this article, Quispel, Roberts and Thompson type of nonlinear partial difference equation with two independent variables is considered and identified five distinct nonlinear partial difference equations admitting continuous point symmetries quadratic in the dependent variable. Using the degree growth of iterates the integrability nature of the obtained nonlinear partial difference equations is discussed. It is also shown how to derive higher order ordinary difference equations from the periodic reduction of the identified nonlinear partial difference equations. The integrability nature of the obtained ordinary difference equations is investigated wherever possible. 相似文献
18.
In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show
how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave
equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding
wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy,
linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations
on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds. 相似文献
19.
S. StalinM. Senthilvelan 《Physics letters. A》2011,375(43):3786-3788
In this Letter, we formulate an exterior differential system for the newly discovered cubically nonlinear integrable Camassa-Holm type equation. From the exterior differential system we establish the integrability of this equation. We then study Cartan prolongation structure of this equation. We also discuss the method of identifying conservation laws and Bäcklund transformation for this equation from the identified exterior differential system. 相似文献
20.
《Journal of Nonlinear Mathematical Physics》2013,20(4):489-504
We discuss nonlocal symmetries and nonlocal conservation laws that follow from the systematic potentialisation of evolution equations. Those are the Lie point symmetries of the auxiliary systems, also known as potential symmetries. We define higher-degree potential symmetries which then lead to nonlocal conservation laws and nonlocal transformations for the equations. We demonstrate our approach and derive second degree potential symmetries for the Burgers' hierarchy and the Calogero–Degasperis–Ibragimov–Shabat hierarchy. 相似文献