Semilinear stochastic evolution equations with multiplicative L'evy noise are considered‎. ‎The drift term is assumed to be monotone nonlinear and with linear growth‎. ‎Unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎As corollaries of ...

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolu...

We give the exposition of a generalized symmetry approach to reduction of initial value problems for nonlinear evolution equations in one spatial variable. Using this approach we classify the initial value problems for third-order evolution equations that admit reduction to Cauchy problems for systems of two ordinary differential equations. These reductions are shown to correspond to higher con...

The invariant subspace method is used to classify a class of systems of nonlinear dispersive evolution equations and determine their invariant subspaces and exact solutions. A crucial step is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that systems of evolution equations admit. A few examples of presenting exact solutions with generalized sepa...

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...

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...