摘要:

Monge-Ampère equations of the form,arise in many areas of fluid and solid mechanics. Here it is shown that in the special case, wherefdenotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre and rotation transformations. This linearization is a generalization of three examples from finite elasticity, involving plane strain and plane stress deformations of the incompressible perfectly elastic Varga material and also relates to a previous linearization of this equation due to Khabirov [7].

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.1

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.2

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Considering the coupled envelope equations in nonlinear couplers, the question of integrability is attempted. It is explicitly shown that Hirota’s bilinear method is one of the simple and alternative techniques to Painlevé analysis to obtain the integrability conditions of the coupled nonlinear Schrödinger (CNLS) type equations. We also show that the coupled Hirota equation introduced by Tasgal and Potasek is the next hierarchy of the inverse scattering solvable CNLS equation. The results are in agreement with the known results.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.3

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 in terms of two uncoupled sine-Gordon models.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.4

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.5

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.6

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A new definition for the electromagnetic field velocity is proposed. The velocity depends on the physical fields.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.7

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum mechanics are not, or at least not what they appear to be; their properties are formulated in a series of Conjectures.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.8

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are deduced from the adjoint representation of the auxiliary spectral problem. It is shown that the Lax operator satisfies ther-matrix relation in the Dirac bracket. Thus, the integrabilities of these resulting systems with the Neumann constraints are obtained.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.9

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

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 Schrüdinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studies show that not all integrable higher dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly the two integrable systems mentioned above do not admit Virasoro type subalgebras, eventhough the other integrable higher dimensional systems do admit such algebras which we have also reviewed in the Appendix. Further, we bring out physically interesting solutions for special choices of the symmetry parameters in both the systems.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.2.10

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor