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A Darboux transformation for the Drinfeld–Sokolov–Satsuma–Hirota system of coupled equations is constructed with the aid of gauge transformations between the Lax pairs. As an application, several types of solutions of the Drinfeld–Sokolov–Satsuma–Hirota system are obtained, including soliton solutions, periodic solutions, rational solutions and others. 相似文献
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《理论物理通讯》2015,(12)
In this letter,we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system. 相似文献
4.
G. A. Kotel'nikov 《Journal of Russian Laser Research》2002,23(6):565-579
An algorithm is proposed for studying the symmetry properties of equations used in theoretical and mathematical physics. The application of this algorithm to the free Schrödinger equation permits one to establish that, in addition to the known Galilei symmetry, the free Schrödinger equation possesses also relativistic symmetry in some generalized sense. This property of the free Schrödinger equation provides an extension of the equation into the relativistic domain of the free particle motion under study. 相似文献
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In this article we characterize a certain class of rational solutions of the hierarchy of master symmetries for KdV. The result
is that the generic rational potentials that decay at infinity and remain rational by all the flows of the master-symmetry
KdV hierarchy are bispectral potentials for the Schr?dinger operator. By bispectral potentials we mean that the corresponding
Schr?dinger operators possess families of eigenfunctions that are also eigenfunctions of a differential operator in the spectral
variable. This complements certain results of Airault–McKean–Moser [4], Duistermaat–Grünbaum [10], and Magri–Zubelli [40].
As a consequence of bispectrality, the rational solutions of the master symmetries turn out to be solutions of a (generalized)
string equation.
Received: 28 January 1999 / Accepted: 22 October 1999 相似文献
6.
《理论物理通讯》2017,(5)
The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons. 相似文献
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LI Zhi-Fang RUAN Hang-Yu 《理论物理通讯》2005,44(3):385-388
A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD) equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lou. These symmetries constitute an infinite-dimensional generalized w∞ algebra. 相似文献
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The Hirota–Satsuma coupled KdV equations associated 2×2 matrix spectral problem is discussed by the dressing method,which is based on the factorization of integral operator on a line into a product of two Volterra integral operators.A new solution is obtained by choosing special kernel of integral operator. 相似文献
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Some remarks on the paper Symmetries and generalized W algebra of the modified KP equation (S. Y. Lou and G. J. Ni, Lett. Math. Phys. 34 (1995), 327–331) are given. It is pointed out that if we consider the inverse operator of a differential operator to be a linear operator, the vector fields nv(f) defined in the above Letter are not certain to be symmetries of the modified KP equation under consideration. 相似文献
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Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation 下载免费PDF全文
Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied, and the expressions of phase shift for lump wave before and after collisions are given. Furthermore, ... 相似文献
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James D. E. Grant 《Communications in Mathematical Physics》2010,296(2):429-446
We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat ${\mathbb{R}^4}$ . We show how all such connections lie in the orbit of the flat connection on ${\mathbb{R}^4}$ under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type. 相似文献
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Anjan Biswas Anwar Ja'afar Muhammad Jawad Wayne N. Manrakhan Amarendra K. Sarma Kaisar R. Khan 《Optics & Laser Technology》2012,44(7):2265-2269
The Schrödinger–Hirota equation governs the propagation of optical solitons in a dispersive optical fiber. In this paper, this equation will be solved by the ansatz method for bright and dark 1-soliton solution. The power law nonlinearity will be assumed. By using the tanh method, some additional solutions will be derived. Finally, the numerical simulations will be given. 相似文献
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Li-yeng Sung 《Mathematical Physics, Analysis and Geometry》1999,2(1):1-24
We prove that the solution of the Cauchy problem for the Kadomtsev–Petviashvili-I Equation obtained by the inverse spectral method belongs to the Sobolev space Hk(R2) for k 0, under the assumption that the initial datum is a small Schwartz function. This solution is shown to be the unique solution within a class of generalized solutions of the Kadomtsev–Petviashvili-I equation. 相似文献
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Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang–Baxter equation with multipermutation level n and an abelian involutive Yang–Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation whose associated involutive Yang–Baxter group is abelian are multipermutation solutions. Earlier the authors proved this with the additional square-free hypothesis on the solutions. It is also proved that finite square-free non-degenerate involutive set-theoretic solutions associated to a left brace are multipermutation solutions. 相似文献
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LIU Ping LOU Sen-Yue 《理论物理通讯》2009,51(1):27-34
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries. 相似文献
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Infinite-Parameter Potential Symmetries and a New Exact Solution for the Particle-Cluster Dynamic Equation 下载免费PDF全文
The master equation of a one-dimensional lattice-gas model with order preservation where the occupation probabilities of sites corresponding to Bose statistics as a consequence of the prescribed dynamics is studied with the potential symmetry method.The infinite-parameter potential symmetry and a new exact solution are obtained.The result illustrates that there remains the possibility of the above nonlinear equation to a linear partial differential equation by a non-invertible mapping. 相似文献
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The discrete spectrum of the nonstationary Schr?dinger equation and localized solutions of the Kadomtsev–Petviashvili-I (KPI)
equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally
decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral
parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI
behave as collection of individual humps with nonuniform dynamics.
Received: 30 September 1998 / Accepted: 30 March 1999 相似文献
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Mohamed Boucetta 《Letters in Mathematical Physics》2008,83(1):69-81
We show that given a finite-dimensional real Lie algebra acting on a smooth manifold P then, for any solution of the classical Yang–Baxter equation on , there is a canonical Poisson tensor on P and an associated canonical torsion-free and flat contravariant connection. Moreover, we prove that the metacurvature of
this contravariant connection vanishes if the isotropy Lie subalgebras of the action are trivial. Those results permit to
get a large class of smooth manifolds satisfying the necessary conditions, introduced by Eli Hawkins, to the existence of
noncommutative deformations.
Recherche menée dans le cadre du Programme Thématique d’Appui à la Recherche Scientifique PROTARS III. 相似文献
20.
《理论物理通讯》2017,(6)
In this paper, we consider the two-dimensional complex Ginzburg–Landau equation(CGLE) as the spatiotemporal model, and an expression of energy eigenvalue is derived by using the phase-amplitude representation and the basic ideas from quantum mechanics. By numerical simulation, we find the energy eigenvalue in the CGLE system can be divided into two parts, corresponding to spiral wave and bulk oscillation. The energy eigenvalue of spiral wave is positive, which shows that it propagates outwardly; while the energy eigenvalue of spiral wave is negative, which shows that it propagates inwardly. There is a necessary condition for generating a spiral wave that the energy eigenvalue of spiral wave is greater than bulk oscillation. A wave with larger energy eigenvalue dominates when it competes with another wave with smaller energy eigenvalue in the space of the CGLE system. At the end of this study, a tentative discussion of the relationship between wave propagation and energy transmission is given. 相似文献