Related papers: Nonlinear acoustic waves in channels with variable…
We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the…
Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A…
An acoustic wave equation for pressure accounting for viscoelastic attenuation is derived from viscoelastic equations of motion. It differs significantly from the equations proposed by Szabo. Dispersion and attenuation associated with the…
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
Transverse elastic waves behave differently in nonlinear isotropic and anisotropic media. Quadratically nonlinear coupling in the evolution equations for wave amplitudes is not possible in isotropic solids, but such a coupling may occur for…
We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The two-component nonlinear variational wave equation…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave vector modulations. The symmetry classification builds on the concept of extended point groups:…
The nonlinear turbulent interactions between acoustic gravity waves are investigated using two dimensional nonlinear fluid simulations. The acoustic gravity waves consist of velocity and density perturbations and propagate across the…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…
We generalize previous \cite{AiBa2} work on the classification of ($C^\infty$) symmetries of plane-fronted waves with an impulsive profile. Due to the specific form of the profile it is possible to extend the group of normal-form-preserving…
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…
We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator…
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…
It is well known that in some cases the spectral parameter has a group interpretation. We discuss in detail the case of Gauss-Codazzi equations for isothermic surfaces immersed in $E^3$. The algebra of Lie point symmetries is 4-dimensional…
We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…