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wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data. The method is model-agnostic in that it does not require explicit knowledge of the underlying…
We show how to approximate a solution of the first order linear evolution equation, together with its possible analytic continuation, using a solution of the time-fractional equation of order $\delta >1$, where $\delta \to 1+0$.
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three…
The discrete gradient approach is generalized to yield integral preserving methods for differential equations in Lie groups.
In this paper we make a study of a partial integral differential equation with $p$-Laplacian using a mixed finite element method. Two stable and convergent fixed point schemes are proposed to solve the nonlinear algebraic system. Using the…
Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
In this paper we study the existence of solutions to an isotropic differential inclusion.
A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…
We present a new and relatively elementary method for studying the solution of the initial-value problem for dispersive linear and integrable equations in the large-$t$ limit, based on a generalization of steepest descent techniques for…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…