# A class of solutions of the generalized Lund–Regge model

01 Nov 1982-Journal of Mathematical Physics (American Institute of Physics)-Vol. 23, Iss: 11, pp 2155-2158

TL;DR: In this paper, a class of solutions for the generalized Lund-Regge model of Corones and its Euclidean counterpart are presented, and a new solution is noted for the original Lund-regge model.

Abstract: A class of solutions are obtained for the generalized Lund–Regge model of Corones [J. Math. Phys. 19, 2431 (1978)] and its Euclidean counterpart. As a consequence, a new solution is noted for the original Lund–Regge model.

##### Citations

More filters

••

[...]

TL;DR: In this paper, the van der Waals-type long-range potential and the quark-confining logarithmic potential are derived for two-dimensional systems of the form I=a0+aiξi + (1)/(2) aijξIξj, i, j=1, 2.

Abstract: General equations are formulated to determine all potentials for two‐dimensional systems of the type L= (1)/(2) ( p21 +p22) −V(q1,q2,t), which admits invariants of the form I=a0+aiξi + (1)/(2) aijξiξj, i, j=1,2, where ξ1 =z=q1+iq2, ξ2=z=q1−iq2, a0, ai, aij are arbitrary functions of t, z=q1+iq2, and z=q1−iq2. Simplifying restrictions reduce the general equation to a tractable form. The resulting equations are solved for a special class of time‐separable potentials and derive (i) the van der Waals‐type long‐range potential, V(r,t)=β(t)(b/r4+d) and (ii) the quark‐confining logarithmic potential, V(r,t)=β(t)λ(ln r+b1/r4+d1). Invariants I for the resulting dynamical systems are found. Some observations on the present method in the context of Katzin and Levine and of Lewis and Leach analyses have also been made.

18 citations

••

[...]

TL;DR: In this paper, the construction of invariants for two-dimensional, time-dependent classical systems has been carried out with special reference to linearly and harmonically confining potentials.

Abstract: The construction of invariants for two-dimensional, time-dependent classical systems has been carried out with special reference to linearly and harmonically confining potentials.

13 citations

••

[...]

TL;DR: In this paper, the construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems, and the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations.

Abstract: The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t−4/3q1/2.

5 citations

••

[...]

TL;DR: In this article, two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of NDEs has been formed wherefrom the previous two sets can be obtained as particular cases.

Abstract: Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang [1] while discussing the condition of self-duality ofSU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature.

5 citations

••

[...]

TL;DR: The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited and two new types of solutions of these equations have been obtained as discussed by the authors.

Abstract: The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited. Two new types of solutions of these equations have been obtained. Each type allows infinite number of solutions. It has also been shown that the chiral invariant field equations admit invariance for a transformation of the dependent variables.

2 citations

##### References

More filters

••

[...]

TL;DR: In this article, a relativistic theory of one-dimensional extended objects interacting through a massless scalar field, of which they are in turn the source, is constructed, and the diverging self-interaction of these objects is regularizable through a renormalization of the slope of the Regge trajectories.

Abstract: A classical relativistic theory of one-dimensional extended objects interacting through a massless scalar field, of which they are in turn the source, is constructed. In the no-coupling limit, the string model is recovered. In another limit, the system that describes nonrelativistic vortex motion in a superfluid is obtained. The diverging self-interaction of these objects is shown to be regularizable through a renormalization of the slope of the Regge trajectories. Motion in an external field is studied in some detail and leads to a system of coupled nonlinear equations that generalizes the sine-Gordon system. Solitary wave solutions to these equations are obtained and a natural geometric interpretation to the associated linear equations of the inverse scattering method is given.

445 citations

••

[...]

TL;DR: In this article, inhomogeneous solutions (pseudoparticles) for the classical two-dimensional ferromagnet were found explicitly, where pseudoparticles do not contribute to the propagating part of the equation of motion.

Abstract: Inhomogeneous solutions (pseudoparticles) for the classical two-dimensional ferromagnet are found explicitly. By the appearance of pseudoparticles the correlation function changes over from power law decay to an exponential one. Pseudoparticles do not contribute to the propagating part of the equation of motion.

14 citations

••

[...]

TL;DR: In this article, the nonlinear coupled equations obtained by Lund and Regge in connection with dynamics of relativistic vortices (or strings) interacting through a scalar field are obtained.

Abstract: Attempts are made to obtain solutions for the nonlinear coupled equations obtained by Lund and Regge in connection with dynamics of relativistic vortices (or strings) interacting through a scalar field.

10 citations

••

[...]

TL;DR: The Lie group framework for soliton equations is illustrated in this paper and it is shown that the original Lund-Regge model is one of an infinite family of similar relativistically invariant models that possess associated eigenvalue problems and isospectral flows.

Abstract: The Lie group framework for soliton equations is illustrated. It is shown that the original Lund–Regge model is one of an infinite family of similar relativistically invariant models that possess associated eigenvalue problems and isospectral flows. The models are explicitly found and their associated structures displayed. The group theoretic significance of the soliton equations and associated structures are given in accordance with the general theory.

8 citations