the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

In this paper we study an initial boundary value problem for Zakharov’s equations, describing the space propagation of a laser beam entering in a plasma. We prove a strong instability result and prove that the mathematical problem is ill-posed in Sobolev spaces. We also show that it is well posed in spaces of analytic functions. Several consequences for the physical consistency of the model are...

The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassic case, linear stability analysis of this dynamical system shows a destabilizing rôle played b...

A new multivariate Toda hierarchy of nonlinear partial differential equations adapted to biorthogonal polynomials is discussed. This integrable associated with non-standard biorthogonality. Wave and Baker functions, linear equations, Lax Zakharov–Shabat KP type appropriate reductions, Darboux or spectral transformations, bilinear involving transformations are presented.

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

We extend the approach of Dolgov and Zakharov to the axial anomaly to study polarized radiative decays. We analyse the pattern of mass singularity cancellation in the corresponding decay rates. We compare polarized and unpolarized cases. The cancellation of the infrared and collinear singularities is verified to all powers of the lepton mass for the π+ and Z0 polarized radiative decays. PACS 11...

We prove existence and uniqueness of solutions to the Klein-Gordon-Zakharov system in the energy space H × L on some time interval which is uniform with respect to two large parameters c and α. These two parameter correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also ab...

Numerical and analysis was used to identify the best code, which is then used to test pure propagation of swells in a coastal region. Furthermore, we have also coded the four wave interaction computation in the nonlinear source function based on the Zakharov formulation. Though the final form still does not have a Homiltonian structure, the formulation resulted in a great reduction of computati...

We analyze typical time scales resulting from the coupled dynamics of high- and low-frequency wave components in solitary solutions of the Zakharov equations. Linear stability analysis around the solitary modes suggests that adiabatic regimes may be obtained in the limit of high- and low-field intensities where the disparity of eigenfrequencies is large. Full simulations, however, reveal that a...