121992 articles

Mingliang WANG, Yubin ZHOU, Zhibin LI

Pages: 120 - 125

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.

Baoqun LU, Yong HE, Guangjiong NI

Pages: 140 - 148

In this paper we give a method to obtain Darboux transformations (DTs) of integrable equations. As an example we give a DT of the dispersive water wave equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek equation.

Wilhelm FUSHCHYCH

Pages: 159 - 161

A new definition for the electromagnetic field velocity is proposed. The velocity depends on the physical fields. The question posed by the title of this paper is, surprisingly, not yet answered uniquely today; not even by way of definition. According to modern assumptions the light is the electromagnetic...

M. SENTHIL VELAN, M. LAKSHMANAN

Pages: 190 - 211

In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schrödinger...

S.G. BINDU, V.C. KURIAKOSE

Pages: 149 - 158

Electromagnetic wave propagation through cold collision free plasma is studied using the nonlinear perturbation method. It is found that the equations can be reduced to the modified Kortweg-de Vries equation.

Marco AMEDURI, Costas J. EFTHIMIOU

Pages: 132 - 139

In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlevé analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model. We are led to the conclusion that the model is not integrable classically, except at a trivial point where the theory can be described...

D.J. ARRIGO, J.M. HILL

Pages: 115 - 119

Monge-Ampère equations of the form, uxxuyy - u2 xy = F(u, ux, uy) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u4 yf(u, ux/uy), where f denotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre...

F. CALOGERO

Pages: 289 - 293

A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian ("acceleration equal force") equations of motion, featuring one-body ("external") and pair ("interparticle") forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate,...

Rafal ABLAMOWICZ

Pages: 294 - 313

We use isomorphism between matrix algebras and simple orthogonal Clifford algebras C (Q) to compute matrix exponential eA of a real, complex, and quaternionic matrix A. The isomorphic image p = (A) in C (Q), where the quadratic form Q has a suitable signature (p, q), is exponentiated modulo a minimal...

Boris A. KUPERSHMIDT

Pages: 245 - 288

Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.

S.Yu. SAKOVICH

Pages: 230 - 233

A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé test for integrability well, and its 4×4 Lax pair with two spectral parameters is found. The results show that the Painlevé classification of coupled KdV equations by A. Karasu...

Peter WALL

Pages: 331 - 348

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form - div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. The sequence (h) tends to 0 and the map a(x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions. It is proved...

Mina B. ABD-EL-MALEK

Pages: 314 - 330

The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the problem of time-dependent vertical temperature...

M.L. GANDARIAS, P. VENERO, J. RAMIREZ

Pages: 234 - 244

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced...

Boris A. KUPERSHMIDT

Pages: 483 - 495

Abstract telegrapher's equations and some random walks of Poisson type are shown to fit into the framework of the Hamiltonian formalism after an appropriate timedependent rescaling of the basic variables has been made.

S.K. PAUL, A. ROY CHOWDHURY

Pages: 349 - 356

N-fold Bäcklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value of N. Lastly it is shown how generalized soliton solutions are generated from...

A.M. HAMZA

Pages: 462 - 470

The fundamental problem of Farley-Buneman turbulence in the auroral E-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroral E-region plasma has to undergo before reaching a steady state. The mode-coupling...

A.M. HAMZA

Pages: 438 - 461

The conventional theory of resonance broadening for a two-species plasma in a magnetic field is revised, and applied to an ionospheric turbulence case. The assumptions made in the conventional theory of resonance broadening have, in the past, led to replacing the frequency by + ik2 D in the resonant...

T.A. IVANOVA

Pages: 396 - 404

Infinite-dimensional algebra of all infinitesimal transformations of solutions of the self-dual Yang-Mills equations is described. It contains as subalgebras the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations.

W.W. ZACHARY, V.M. SHTELEN

Pages: 417 - 437

A concept of asymptotic symmetry is introduced which is based on a definition of symmetry as a reducibility property relative to a corresponding invariant ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle Schrödinger equation, discovered by Fushchych and Segeda in 1977, can...

Peter E. HYDON

Pages: 405 - 416

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism...

J. CASAHORRÁN

Pages: 371 - 382

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise,...

A.A. BORGHARDT, D.Ya. KARPENKO

Pages: 357 - 363

The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the characteristic representation technique, the Schwinger integral...

Ahmet SATIR

Pages: 364 - 370

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.

R. MARTINI, P.K.H. GRAGERT

Pages: 1 - 4

We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed.

Zhimin JIANG

Pages: 5 - 12

An eigenvalue problem with a reference function and the corresponding hierarchy of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite-dimensional completely integrable...

Samir F. RADWAN

Pages: 13 - 34

The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical...

V.A. TROTSENKO

Pages: 35 - 50

A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics [1][6]. In the present paper, using the variational method for solving nonlinear boundary problems of statics of hyper-elastic membranes under the regular...

Takeo KOJIMA

Pages: 99 - 119

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions (x1, 0) (x2, t) ±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x1 = 0, we express...

P. RUDRA

Pages: 51 - 65

Symmetry classification of two-body central potentials in a two-particle Schrödinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem...

Peter A. CLARKSON, Thomas J. PRIESTLEY

Pages: 66 - 98

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = u + u2 xx + uuxxxx + µuxxtt + uxuxxx + u2 xx, (1) where , , , and µ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm...

Boris A. KUPERSHMIDT

Pages: 222 - 245

The multiplication in the Virasoro algebra [ep, eq] = (p - q)ep+q + p3 - p p+q, p, q Z, [, ep] = 0, comes from the commutator [ep, eq] = ep eq - eq ep in a quasiassociative algebra with the multiplication ep eq = q(1 + q)

Denis BLACKMORE, Roman SAMULYAK, Anthony ROSATO

Pages: 198 - 221

A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian...

A.N. LEZNOV

Pages: 181 - 197

Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental representations of the corresponding semisimple groups.

R. RADHA, S. VIJAYALAKSHMI, M. LAKSHMANAN

Pages: 120 - 126

In this letter, we report the existence of a novel type of explode-decay dromions, which are exponentially localized coherent structures whose amplitude varies with time, through Hirota method for a nonisospectral Davey-Stewartson equation I discussed recently by Jiang. Using suitable transformations,...

N.P. LANDSMAN

Pages: 161 - 180

We attempt to reconstruct the irreducible unitary representations of the Banach Lie group U0(H) of all unitary operators U on a separable Hilbert space H for which U - I is compact, originally found by Kirillov and Ol'shanskii, through constrained quantization of its coadjoint orbits. For this purpose...

A.V. SHAPOVALOV, A.Yu. TRIFONOV

Pages: 127 - 138

A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schrödinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics...

S. MELKONIAN

Pages: 139 - 160

The cubic Hénon-Heiles system contains parameters, for most values of which, the system is not integrable. In such parameter regimes, the general solution is expressible in formal expansions about arbitrary movable branch points, the so-called psi-series expansions. In this paper, the convergence of...

Anatoliy K. PRYKARPATSKY, Denis BLACKMORE

Pages: 246 - 254

If we are given a smooth differential operator in the variable x R/2Z, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S1 )-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal...

Boris A. KUPERSHMIDT

Pages: 269 - 272

If a classical r-matrix r is skewsymmetric, its quantization R can lose the skewsymmetry property. Even when R is skewsymmetric, it may not be unique.

Boris A. KUPERSHMIDT, Ognyan S. STOYANOV

Pages: 344 - 354

A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits.

S.Yu. SAKOVICH

Pages: 255 - 262

It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlevé test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown.

P. BRACKEN, A. M. GRUNDLAND

Pages: 294 - 313

Analysis of the generalized Weierstrass-Enneper system includes the estimation of the degree of indeterminancy of the general analytic solution and the discussion of the boundary value problem. Several different procedures for constructing certain classes of solutions to this system, including potential,...

Philippe CHANFREAU, Hannu LYYJYNEN

Pages: 314 - 331

This paper aims to cast some new light on controlling chaos using the OGY- and the Zero-Spectral-Radius methods. In deriving those methods we use a generalized procedure differing from the usual ones. This procedure allows us to conveniently treat maps to be controlled bringing the orbit to both various...

L.A. KHODARINOVA, I.A. PRIKHODSKY

Pages: 263 - 268

Explicit algebraic relations between the quantum integrals of the elliptic Calogero Moser quantum problems related to the root systems A2 and B2 are found.

Partha GUHA

Pages: 273 - 293

In this paper we discuss a universal integrable model, given by a sum of two WessZumino-Witten-Novikov (WZWN) actions, corresponding to two different orbits of the coadjoint action of a loop group on its dual, and the Polyakov-Weigmann cocycle describing their interactions. This is an effective action...

F. DELDUC, L. GALLOT

Pages: 332 - 343

We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We...

Boris A. KUPERSHMIDT

Pages: 448 - 488

The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, where the standard definitions are shown to be deficient, is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks...

Christodoulos SOPHOCLEOUS

Pages: 355 - 364

We consider the one-dimensional porous medium equation ut = (un ux)x + µ x un ux. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction...

Yuri B. SURIS

Pages: 411 - 447

We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the r-matrix framework. An r-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All relativistic constructions are regular one-parameter perturbations of...