Showing papers in "Physica D: Nonlinear Phenomena in 1981"

TL;DR: In this paper, it was shown that compatible symplectic structures lead in a natural way to hereditary symmetries, and that a hereditary symmetry is an operator-valued function which immediately yields a hierarchy of evolution equations, each having infinitely many commuting symmetry all generated by this hereditary symmetry.

TL;DR: In this article, a series of τ functions parametrized by integers are introduced and their ratios to the original τ function are then shown to be explicit rational expressions in terms of the coefficients of A(x).

TL;DR: In this paper, a unified treatment of monodromy and spectrum-preserving deformations is presented, in particular a general procedure is described to reduce the latter into the former consistently, and the concept of the τ-function, previously introduced for the former, is extended to the isospectral context.

TL;DR: In this article, a general theory of monodromy preserving deformation is developed for a system of linear ordinary differential equations d Y d x =A(x)Y, where A ( x ) is a rational matrix.

TL;DR: In this article, the problem of reduction for systems of nonlinear equations integrable by the inverse scattering method is discussed and an infinite set of conservation laws is constructed for the system of equations for a two-dimensional Toda chain, the inverse problem is solved and exact N-soliton solutions are found.

TL;DR: In this article, a Poisson structure for the Yang-Mills-Vlasov equations was derived by using general methods of symplectic geometry and the main ingredients of the construction were the symplectic structure on the co-adjoint orbits for the group of canonical transformations.

TL;DR: In this paper, the quantum mechanics of pseudointegrable systems are studied in detail by computing energy levels using an exact formalism, and the Weyl area rule plus edge and corner corrections gives a very accurate approximation for the mean level density.

TL;DR: In this article, the two-soliton systems of the perturbed non-linear Schrodinger (NLS) and sine-Gordon (SG) equations are considered by means of a simple particle approach in which the soliton interaction and the action of an external perturbation are described by the one-solon perturbations theory.

TL;DR: In this paper, it was shown that in an arbitrary Lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities, a Lagrangians may be introduced analogous to that for classical particles with a pair interaction potential.

TL;DR: In this article, the authors investigated numerically the behavior of periodic orbits of reversible area-preserving maps of the plane and found that the pattern of periodic points reproduces itself, asymptotically, from one bifurcation to the next when the scale is expanded by α = −4.018076704 and β = 16.363896879.

TL;DR: A collisionless Boltzmann equation, describing long waves in a dense gas of particles interacting via short-range forces, is shown to be equivalent to the Benney equations, which describe long wave in a perfect two-dimensional fluid with a free surface as mentioned in this paper.

TL;DR: In this article, the effect of diffraction and dispersion on three wave coupling is investigated and the existence of stable three-dimensional solitons is shown, which is similar to modulational instability of quasimonochromatic waves.

TL;DR: In this article, the dynamics of sine-Gordon solitons in two spatial dimensions are studied and new results like 4π-break up, solon-on-soliton effect, and scattering at a circular inhomogeneity are reported.

TL;DR: In this article, the τ-function related to a Hamiltonian is defined and the correlation function given in the study of the two-dimensional Ising model is a τ function for the third Painleve equation, and the list of the Hamiltonians which are polynomials in the two canonical variables is given.

TL;DR: In this article, the discretisation of the ordinary nonlinear differential equation d y d t = y(1−y) by the entral difference scheme is studied for fixed mesh size.

TL;DR: In this paper, the long-time behavior of solutions of the Korteweg-deVries, modified Kordeweg deVries (mKdV) or sine-Gordon equations that evolve from given initial data on -∞

TL;DR: In this article, numerical studies of Davydov's nonlinear dynamic model for the α-helix protein confirm his prediction of soliton formation, which is robust localized dynamic entities that couple molecular (amide-I) vibrations to longitudinal sound waves.

TL;DR: The class of exactly integrable non-linear evolution equations related to the general first order n × n linear problem is studied in this paper, where the set of independent scattering data J is determined and trace identities are obtained.

TL;DR: In this article, the authors studied the functional dependence of the coordinate q on the canonical angle variable θ in the complex θ-plane, where natural boundaries are found at constant absolute values of Im θ.

TL;DR: In this article, a sequence of period doubling bifurcations of periodic orbits of Henon's conservative two-dimensional mapping was studied numerically and it was shown that such sequences possess universality properties, similar to the ones observed for dissipative systems.

TL;DR: Theory of motion of quasi-particles, electrons and a vibrational excitation along molecular chains is developed without using the adiabatic approximation and the perturbation theory.

TL;DR: A survey of the applications of catastrophe theory to the physical sciences can be found in this paper, where the authors confine attention to an area lying between "elementary" and "general" catastrophe theory, usually known as Singularity Theory.

TL;DR: In this article, the authors studied the situation in which flutter and divergence become coupled, and showed that there are essentially two ways in which this is likely to occur, in the first case the system can be reduced to an essential model which takes the form of a single degree of freedom nonlinear oscillator.

TL;DR: In this article, the XYZ Heisenberg model is considered from the stand-point of the quantum inverse problem method and it is shown that this model is a completely integrable quantum system Algebraic generalization of the Bethe Ansatz for finding eigenvectors and eigenvalues of the Hamiltonian of the XZ model.

TL;DR: In this paper, the authors examined the effect of local spatial changes of nerve axon geometry such as diameter increase and branching, may cause that action potential waves approaching a region of geometric change fail to propagate beyond it.

TL;DR: In this article, it was shown that one-parameter families of area-preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter, and that the scaling transformation Λ: R 2→ R 2 is conjugate to the transformation λ0:(x, y)→(λx, μy), with λ2 ≠ μ, and in fact λ 2 >μ.