共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal of Nonlinear Mathematical Physics》2013,20(2):193-204
Abstract For the first time we show that the quasiclassical limit of the symmetry constraint of the Sato operator for the KP hierarchy leads to the generalized Zakharov reduction of the Sato function for the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the dKP hierarchy recently. By either regarding the symmetry constrained dKP hierarchy as its stationary case or taking the dispersionless limit of the KP hierarchy with self-consistent sources directly, we construct a new integrable dispersionless hierarchy, i.e., the dKP hierarchy with self-consistent sources and find its associated conservation equations (or equations of Hamilton-Jacobi type). Some solutions of the dKP equation with self-consistent sources are also obtained by hodograph transformations. 相似文献
2.
We discuss the dressing formulation and twistor construction for the dispersionless Dym (dDym) hierarchy. In particular, we investigate one-variable and two-variables reductions of the dDym hierarchy to illustrate the formalism. We derive the associated string equations of the reduced dDym hierarchies and obtain their hodograph solutions. 相似文献
3.
The Vlasov equation governs the evolution of the single-particle probability distribution function (PDF) for a system of particles interacting without dissipation. Its singular solutions correspond to the individual particle motions. The operation of taking the moments of the Vlasov equation is a Poisson map. The resulting Lie-Poisson Hamiltonian dynamics of the Vlasov moments is found to be integrable is several cases. For example, the dynamics for coasting beams in particle accelerators is associated by a hodograph transformation to the known integrable Benney shallow-water equation. After setting the context, the Letter focuses on geodesic Vlasov moment equations. Continuum closures of these equations at two different orders are found to be integrable systems whose singular solutions characterize the geodesic motion of the individual particles. 相似文献
4.
The symmetry constraint for dispersionless Harry Dym (dHD) hierarchy is derived for the first time by taking dispersionless limit of that for 2+1 dimensional Harry Dym hierarchy. Then, the dHD is extended by means of the symmetry constraint which we derived. From the zero-curvature equation of the new extended dHD hierarchy, two types of dHD equations with self-consistent sources (dHDESCS) together with their associated conservation equations are obtained. Moreover, the hodograph solutions to the first type of dHDESCS are given. Finally, Bäcklund transformation between the extended dispersionless mKP hierarchy and extended dHD Hierarchy are also constructed. 相似文献
5.
《Physics letters. A》1999,256(1):39-46
The integrable lattice equations arising in the context of singular manifold equations for scalar, multicomponent KP hierarchies and 2D Toda lattice hierarchy are considered. They generate the corresponding continuous hierarchy of singular manifold equations, its Bäcklund transformations and different forms of superposition principles; their distinctive feature is invariance under the action of Möbius transformation. Geometric interpretation of these discrete equations is given. 相似文献
6.
Antonio Moro 《Physics letters. A》2009,373(34):3021-3023
Vortices are screw phase dislocations associated with helicoidal wave-fronts. In nonlinear optics, vortices arise as singular solutions to the phase-intensity equations of geometric optics. They exist for a general class of nonlinear response functions. In this sense, vortices possess a universal character. Analysis of geometric optics equations on the hodograph plane leads to deformed vortex type solutions that are sensitive to the form of the nonlinearity. The case of a Kerr type nonlinear response is discussed as a specific example. 相似文献
7.
Shoufeng Shen Bao-Feng Feng Yasuhiro Ohta 《Journal of Nonlinear Mathematical Physics》2017,24(2):195-209
In this paper, we are concerned with a modified complex short pulse (mCSP) equation of defocusing type. Firstly, we show that the mCSP equation is linked to a complex coupled dispersionless equation of defocusing type via a hodograph transformation, thus, its Lax pair can be deduced. Then the bilinearization of the defocusing mCSP equation is formulated via dependent variable and hodograph transformations. One- and two-dark soliton solutions are found by Hirota’s bilinear method and their properties are analyzed. It is shown that, depending on the parameters, the dark soliton solution can be either smoothed, cusponed or looped one. More specifically, the dark soliton tends to be evolved into a singular (cusponed or looped) one due to the increase of the spatial wave number in background plane waves and the increase of the depth of the trough. In the last part of the paper, we derive the defocusing mCSP equation from the single-component extended KP hierarchy by the reduction method. As a by-product, the N-dark soliton solution in the form of determinants for the defocusing mCSP is provided. 相似文献
8.
F. S. Uliu 《Annalen der Physik》1973,29(4):375-384
In this paper the LEHMANN-SYMANZIK-ZIMMERMANN (L. S. Z.) structure of the {n; 3} sector of the LEE model is investigated and some general features of the {n; k} sector are presented. It is shown that the {n; k} sector with k ≤ n is entirely determined by the solutions of k singular integral equations. In the case of the sector {k — l; k} with l integer, 1 ≥ l ≤ k – 1, k – l singular integral equations must be solved in order to determine all physical quantities. 相似文献
9.
Based on the dispersionless KP (dKP) theory, we study a topological Landau-Ginzburg (LG) theory characterized by a rational
potential. Writing the dKP hierarchy in a general form treating all the primaries in an equal basis, we find that the hierarchy
naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having a finite number
of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with
those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue
formulae for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation.
The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational
effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase
space.
Supported in part by NSF grant DMS-9403597. 相似文献
10.
F. S. Uliu 《Annalen der Physik》1970,480(4):347-361
In this work the Lehmann-Symanzik-Zimmermann treatment of the (n, 2) sector of the Lee model is given. All physical quantities are expressed by means of the τ-functions. It is found that the solutions of two singular integral equations solve the entire sector. 相似文献
11.
《Physics letters. A》2020,384(2):126064
The hodograph transformation is generally used in order to associate a system of linear partial differential equations to a system of nonlinear (quasilinear) differential equations by interchanging dependent and independent variables. Here we consider the case when the nonlinear differential system can be derived from a Lagrangian density and revisit the hodograph transformation within the formalism of the Lagrangian-Hamiltonian continuous dynamical systems.Restricting to the case of nondissipative, nondispersive one-dimensional waves, we show that the hodograph transformation leads to a linear partial differential equation for an unknown function that plays the role of the Lagrangian in the hodograph variables. We then define the corresponding hodograph Hamiltonian and show that it turns out to coincide with the wave amplitude. i.e., with the unknown function of the independent variables to be solved for in the initial nonlinear wave equation. 相似文献
12.
A class of elliptic–hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes in this way is the extended projective disc, which is Riemannian at ordinary points, Lorentzian at ideal points, and singular on the absolute. Harmonic fields on such a metric can be interpreted as the hodograph image of extremal surfaces in Minkowski 3-space. This suggests an approach to generalized Plateau problems in three-dimensional space-time via Hodge theory on the extended projective disc. Analogous variational problems arise on Riemannian–Lorentzian flow metrics in fiber bundles (twisted nonlinear Hodge equations), and on certain Riemannian–Lorentzian manifolds which occur in relativity and quantum cosmology. The examples surveyed come with natural gauge theories and Hodge dualities. This paper is mainly a review, but some technical extensions are proven. 相似文献
13.
Due to Poinsot’s theorem, the motion of a rigid body about a fixed point is represented as rolling without slipping of the moving hodograph of the angular velocity over the fixed one. If the moving hodograph is a closed curve, visualization of motion is obtained by the method of P.V. Kharlamov. For an arbitrary motion in an integrable problem with an axially symmetric force field the moving hodograph densely fills some two-dimensional surface and the fixed one fills a three-dimensional surface. In this paper, we consider the irreducible integrable case in which both hodographs are two-frequency curves. We obtain the equations of bearing surfaces, illustrate the main types of these surfaces. We propose a method of the so-called non-straight geometric interpretation representing the motion of a body as a superposition of two periodic motions. 相似文献
14.
G. Costanza 《Physica A》2009,388(13):2600-2622
The continuum evolution equations are derived from updating rules for three classes of stochastic models. The first class corresponds to models whose stochastic continuum equations are of the Langevin type obtained after carrying out a “local average” known as coarse-graining. The second class consists of a hierarchy of continuum equations for the correlations of the dynamical variables obtained after making an average over realizations. This average generates a hierarchy of deterministic partial differential equations except when the dynamical variables do not depend on the values of the neighboring dynamical variables, in which case a hierarchy of ordinary differential equations is obtained. The third class of evolution equations for the correlations of the dynamical variable constitutes another hierarchy after calculating an average over both realizations and all the sites of the lattice. This double average generates a hierarchy of deterministic ordinary differential equations. The second and third classes of equations are truncated using a mean field (m,n)-closure approximation in order to obtain a finite set of equations. Illustrative examples of every class are given. 相似文献
15.
《Physics letters. A》1998,249(3):204-208
We present new supersymmetric integrable extensions of the a = 4, N = 2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generates a new hierarchy of integrable equations, for which we investigate the Hamiltonian structure. In a special case our system describes the interaction of the KdV equation with the two MKdV equations. 相似文献
16.
Tu Gui-Zhang 《Physics letters. A》1983,94(8):340-342
A new hierarchy of pairs of coupled nonlinear evolution equations is proposed. The first pair of coupled equations can be reduced to the single equation wtt - wtx ± 4ew = 0. It is shown that the equations in this hierarchy possess an infinite number of conserved densities, and that a degenerate symplectic structure can be introduced to the whole hierarchy. 相似文献
17.
The modified Boussinesq hierarchy associated with the 3×3 matrix spectral problem is derived with the help of Lenard recursion equations. Based on the characteristic polynomial of Lax matrix for the modified Boussinesq hierarchy, we introduce an algebraic curve Km−1 of arithmetic genus m−1, from which we establish the associated Baker-Akhiezer function, meromorphic function and Dubrovin-type equations. The straightening out of various flows is exactly given through the Abel map. Using these results and the theory of algebraic curve, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic function, and in particular, that of solutions for the entire modified Boussinesq hierarchy. 相似文献
18.
《Nuclear Physics B》2005,706(3):518-530
We study the relation between the WDVV equations and the τ-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the nontrivial equation for τ-function of the NC KP hierarchy, while the prepotential in the Seiberg–Witten (SW) theory has been identified to the τ-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show explicitly that Whitham hierarchy includes commutative Toda/KP hierarchy. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory. 相似文献
19.
E. Papageorgiu 《Zeitschrift fur Physik C Particles and Fields》1995,65(1):135-150
Starting from a complete set of possible parametrisations of the quark-mass matrices that have the maximum number of texture zeros at the grand unification scale, and the Georgi-Jarlskog mass relations, we classify the neutrino spectra with respect to the unknown structure of the heavy Majorana sector. The results can be casted into a small number of phenomenologically distinct classes of neutrino spectra, characterised by universal mass-hierarchy and oscillation patterns. One finds that the neutrino masses reflect the natural hierarchy among the three generations and obey the quadratic seesaw, for most GUT models that contain a rather “unsophisticated” Majorana sector. A scenario withv τ as the missing hot dark matter component andv e ?v µ oscillations accounting for the solar neutrino deficit comes naturally out of this type of models and is very close to the experimental limit of confirmation or exclusion. In contrast, in the presence of a strong hierarchy of heavy scales or/and some extra symmetries in the Majorana mass matrix, this natural hierarchy gets distorted or even reversed. This fact can become a link between searches for neutrino oscillations and searches for discrete symmetries close to the Planck scale. 相似文献
20.
《Physics letters. A》1987,122(2):95-99
We consider an N-component hierarchy of nonlinear evolution equations, previously known to be bi-hamiltonian and completely integrable. We show that there exist not just two, but (N + 1) compatible hamiltonian structures for this hierarchy. For the case N = 2 we relate our equations to a tri-hamiltonian hierarchy introduced by Kupershmidt. 相似文献