Related papers: The equations of some dispersionless limit
We discuss the numerous advantages of using dimensionless equations in non-relativistic quantum mechanics. Dimensionless equations are considerably simpler and reveal the number of relevant parameters in the models. They are less prone to…
Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…
It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same $q$. In this paper, the existence of composite system with different $q$ subsystems is investigated by fitting the…
A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.
A complete description of $Q$-conditional symmetries of reaction-diffusion-convection equation with arbitrary power nonlinearities is finished. It is shown that the results obtained in the first and second parts of this work (see…
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of $p$-laplacian type is addressed. It is formulated in terms of certain moments of underlying Young measures associated with main…
In this paper, an extended nonlinear Schrodinger equation with higher-order that includes fifth-order dispersion with matching higher-order nonlinear terms is investigated under zero boundary condition at infinity. Carrying out the spectral…
We expand the class of linear symmetric equations for which large sets with no non-trivial solutions are known. Our idea is based on first finding a small set with no solutions and then enlarging it to arbitrary size using a…
In this note we discuss the nature of gaps in the support of a discretely infinitely divisible distribution from the angle of compound Poisson laws/processes. The discussion is extended to infinitely divisible distributions on the…
In this overview paper, we investigate the dispersion of electromagnetic waves for dissipative and non-dissipative dielectric-magnetic uniaxial mediums. Changing the sign of one component of dielectric permittivity ({\epsilon}) or magnetic…
A method is proposed of obtaining (2+1)-dimensional non- linear equations with non-analytic dispersion relations. Bilocal formalism is shown to make it possible to represent these equations in a form close to that for their counterparts in…
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…
We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
We obtain novel nonlinear Schr\"{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…