Sentence examples for equations possesses from inspiring English sources

Wu and Geng, [9], showed early on that the hierarchy of differential-difference equations possesses Hamiltonian structures while a Darboux transformation for the discrete spectral problem is shown to exist.

In the first step, by projection on the finite dimensional orthonormal basis of (mathbf{H}^{mathbf{1}}(boldsymbol{Omega})), we construct a sequence of approximate equations, each of these equations possesses a solution via the Cauchy-Lipschitz criteria.

The Sobolev equations possess the important physical background.

The respective constitutive equations possess general structure (with coupling terms).

The equations possess interesting steady states of lake at rest as well as moving equilibrium states.

It follows that a type of new integrable hierarchy of evolution equations, possessing bi-Hamiltonian structure, is obtained.

By the method used in the proof of Theorem 1 we can easily construct equations possessing a quickly oscillatory solution.

By using the mountain pass theorem and Ekeland's variational principle, we see that such equations possess two solutions.

These partial differential equations possess highly nonlinear source terms, and exhibit strong quenching singularities which pose severe challenges to the design and analysis of highly reliable schemes.

In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form.

The majority of known Darboux-integrable semidiscrete equations possess x- and n-rings of dimensions not exceeding five (see [14, 16, 19]).