We have recently solved the inverse scattering problem for one parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations connected with the commutation of multidimensional vector fields, like the heavenly equation of Plebanski, the dispersionless Kadomtsev Petviashvili (dKP)...

This paper extends the derivation of the Lagrangian averaged Euler (LAEα) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-α equations is simplified and clarified. The derivation in this ...

A nonlinearly realized supersymmetric action describing the invariant couplings of the Goldstino to matter is constructed. Using the Akulov-Volkov Lagrangian, any operator can be made part of a supersymmetric invariant action. Of particular interest are interaction terms which include the product of the Akulov-Volkov Lagrangian with the ordinary matter Lagrangian as well as the coupling of the ...

We investigate the existence of Intrinsic Localized Modes (ILMs) in nonlinear one-dimensional KleinGordon chains. We use the Lagrangian averaging approach parameterizing ILM by several slow-varying variables, and apply the averaging directly in the action principle. Our preliminary studies yield results for ILM dynamics in accordance with those obtained by other methods.

The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars–Toda type and define the Bäcklund auto-transformations for the class of two-component hyperbolic systems.

A gauge-invariant form of the nonlinear Hodge equations is studied. 1991 MSC: 58E15 (Classical field theory)

We apply the (direct and inverse) prolongation method to a couple of non-linear Schrödinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system under consideration, we develop a proce...

The “elliptic” version of a three-dimensional nonlinear integrable equation, the Toda chain equation, is studied by means of the inverse scattering method. Several classes of decaying solutions corresponding to both the continuous and discrete spectrum of the associated spectral problem are obtained. Conditions that guarantee reality and analyticity along with relevant estimates are also given....

Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing i...

We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field.