Theory Of Nonlinear Wave Propagation Research Articles

Nonlinear waves in superposed fluids

A weakly nonlinear theory of wave propagation in superposed fluids in the presence of magnetic fields is presented in this paper. We derive the equations governing the evolution of the amplitude of the progressive as well as the standing waves. It is demonstrated that the waves can be unstable against modulation in the presence of the magnetic fields. We also obtain the nonlinear cut off wave number which separates the region of stability from instability.

Some comments on wave motions described by non-homogeneous quasilinear first order hyperbolic systems

In this paper a quasilinear first order hyperbolic system of partial differential equations involving a source term is considered. Thus in the usual context of the n-dimensional nonlinear wave propagation theory it is shown that the source term may produce attenuation effects against the typical nonlinear steepening of the waves. Therefore, by generalizing Whitham's ideas[9], [10], it is possible to introduce a «reduced system» of field equations which gives an approximate description of the wave process. Then, in an asymptotic way, it is possible to point out that in a wave motion governed by the reduced system there is a coupling between nonlinearity and dissipative (or dispersive) effects. A typical physical example where the present theory may be applied is shown at the end of the paper.

Extension of weakly nonlinear theory of solitary wave propagation

A localized wave propagating horizontally at speed c through a fluid of arbitrary depth H which consists of a lower vertical layer (thickness L) with a weak-depth-dependent density below an upper layer of constant density is considered. The flow is characterized by Long’s equation for the stream function ψ. Exact analytic results are obtained for ψ through O[1/(h−1)] and the wave speed through order O[1/(h−1)2], h=H/L. The terms in ψ of O[1/(h−1)2] are obtained numerically. Using these results the range of validity of such a perturbative approach is examined.

An initial value problem in the theory of nonlinear wave propagation

An initial value problem in the theory of nonlinear wave propagation

Exceptional Waves and Characteristic Shocks on Non-Linear Relativistic Strings

Euler-Lagrange equations of a relativistic massive string are analysed from the stand­ point of non-linear wave propagation theory. Complete exceptionality is shown to hold, while strict exceptionality (usual in non-linear physical theories) appears only for non­ vanishing value of the masses at the ends, when time-like or light-like gauge specification is employed. § 1. Physical characters and applications of string-like models The study of relativistic stringv played quite a significant role in the recent development of hadrodynamics and strong field theory. The capability of Nambu string model) of reproducing the main results of high energy strong interaction phenomenology as: a) Regge behaviour and linearly rising Regge trajectories 3) b) The structure of dual resonance models (DRM) 4) c) A Hagedorn-like state density distribution 5) suggested the idea that the hadrons could be thought like extended structures and in particular one space dimensional. In fact some attempts of generalizing the string model to an N-dimensional system showed that for N> 1 either the linearity of Regge trajectories 6) or the Hagedorn-like distribution is lost.n In the following years the programme of finding a string theory for every known dual model has been carried out. It has been shown that the open string predicts the usual Veneziano amplitude, while the closed string is related to the Shapiro-Virasoro model 8) and the pomeron. The introduction of spin degrees of freedom (Iwasaki and Kikkawa) o) allowed obtaining the super gauge conditions appearing in the mod­ els of Ramond 101 and Neveu-Schwarz.ll) All the previous systems are ghost-free, but exhibit tachyons in the mass spectrum and predict an unphysical dimensionality of space-time (D>4). Recently some results have been obtained in the direction of more physical models.l2) From the point of view of usual field theory the appearance of extended n The author is a member of the G.N.F.M. of the C.N.R. ttl Also Istituto Nazionale di Fisica Nucleare, Sez. di Bologna.

Theory of non-linear wave propagation with application to the interaction and inverse problems

The propagation of non-linear deformation waves in a dissipativc medium is described by a unified asymptotic theory, making use of wave front kinematics and the concepts of progressive waves. The mathematical models are derived from the theories of thermoclasticity or viscoclasticity taking into account the geometric and physical non-linearities and dispersion. On the basis of eikonal equations for the associated linear problem the transport equations of the nth order are obtained. In the multidimensional case the method of matched separation of initial equations is proposed. The interaction problems which occur in head-on collisions and in reflection from boundaries or interfaces are analyzed. Conditions are also studied when the interaction of non-linear waves does not take place. The inverse problem of determining materials properties according to pulse shape changes is discussed.

New approach to the asymptotic theory of nonlinear oscillations and wave-propagation

New approach to the asymptotic theory of nonlinear oscillations and wave-propagation

Wave packet formulation of nonlinear plasma wave kinetics

A theory of nonlinear plasma wave propagation is presented which contains, as particular cases, both the nonlinear Schrödinger equation for coherent waves and the kinetic wave equation for weak plasma turbulence. Fluctuations are represented as a superposition of “micro” wave packets, with finite spread but negligible overlap in wavenumber and frequency. For the case of coherent wave propagation a nonlinear Schrödinger equation is derived, generalized over precious versions in that linear Landau damping nonlinear frequency shift, nonlinear damping, and three-dimensional effects are all included, as well as the non-local, non-Markovian interaction characteristic of this equation. In the case of weak plasma turbulence, the kinetic wave equation is generalized to include self-interaction of the micro packets, which, just as in the coherent case, results in non-local, non-Markovian terms, not heretofore considered in weak turbulence formulations.

Asymptotic Theory of Nonlinear Wave Propagation

By extending the asymptotic method of G. E. Kuzmak, J. C. Luke has shown how G. B. Whitham’s theory of nonlinear wave propagation can be derived directly from the partial differential equation without using the variational principle, in special cases. We apply the same method to a more general class of nonlinear second order partial differential equations or systems of first order equations containing a small parameter e and obtain asymptotic expansions of the solutions.

Non-linear theory of sound propagation through a random medium

The non-linear theory of wave propagation through a random medium is discussed. A renormalized equation for the mean wave field is derived for cases where the wavelength exceeds the correlation scale of the random fluctuations of the medium. This is used to predict shock thickness due to the balance between non-linear terms and dissipation caused by thermal scattering.

Nonlinear wave processes in electrodynamics

This paper gives a brief review of work in the Soviet Union, relevant to the Discussion Meeting on Nonlinear Theory of Wave Propagation in Dispersive Systems (Lighthill 1967) and complementary to the review of work on the subject in other countries presented in the report of that Discussion Meeting.

Perturbation theory of nonlinear elastic wave propagation

In this article a perturbation method is given for obtaining uniformly valid approximations to the solution of problems of plane wave propagation in finite elasticity theory. Examples are given showing its application to problems of longitudinal and shear wave propagation, including an explicit numerical example concerning the propagation of a shear wave in a polyurethane foam rubber.

The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channels

The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channels