The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth and seventh order are obtained. The efficiency of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstr...

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order methods allow large step sizes for highly oscillatory equations when the evolution operators vary slowly in time. The methods are also conservative for equations such as the Schrr odinger equation, where the evolution operator is skew-selfadjoint.

Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction ter...

Root-operator factorization à la Dirac provides an effective tool to deal with equations, which are not of evolution type, or are ruled by fractional differential operators, thus eventually yielding evolution-like equations although for a multicomponent vector. We will review the method along with its extension to root operators of degree higher than two. Also, we will show the results obtained...

This article addresses the various mathematical and statistical properties of Burr type XII distribution (such as quantiles, moments, moment generating function, hazard rate, conditional mean residual lifetime, past deviation about median, stochasic ordering, stress-strength parameter, entropies, Bonferroni Lorenz curves order statistics) are derived. We discuss some exact expressions recurrenc...

Q evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q evolution equations for parton-distribution and fragmentation functions. Because the equations cannot b...

We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

‎this paper presents an application of partial differential equations(pdes) for the segmentation of abdominal and thoracic aortic in cta datasets. an important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. level sets are part of an important class of methods that utilize partial differential equations (pdes) and have been exte...