[en] The q-difference Painlevé II equation admits special solutions written in terms of determinants whose entries are the general solution of the q-Airy equation. An ultradiscrete limit of the special solutions is studied using the procedure of ultradiscretization with parity variables. Then we obtain new Airy-type solutions of the ultradiscrete Painlevé II equation with parity variables, and the solutions have a richer structure than the known solutions. (paper)

No abstract available

[en] It is proved that every smooth function of a real variable with compact support is a convolution of two functions of the same type. Generalizations of this result to other function classes are presented

[en] Oskolkov's system of equations with a cubic source is considered; this describes the dynamics of a viscoelastic fluid. Local solvability (with respect to time) of the problem in the weak generalized sense is proved. Some conditions on the initial function which ensure that the solution blows up in finite time are found, and two-sided estimates for the existence time of the solution are obtained. Moreover, sufficient conditions for the global solvability (with respect to time) of the problem are found. Bibliography: 19 titles.

[en] In the preceding paper of the author parametrizing functions Fi, Th, Ro were introduced depending on word variables, positive-integer variables, and variables whose values are finite sequences of positive-integer variables. With the help of the parametrizing functions Fi, Th, Ro finite formulae are written out for the family of solutions of every equation of the form φ(x₁,x₂,x₃) x₄=ψ(x₁,x₂,x₃) x₅, where φ(x₁,x₂,x₃) and ψ(x₁,x₂,x₃) are arbitrary words in the alphabet x₁, x₂, x₃ in a free monoid.

[en] The existence of infinitely many subharmonic solutions is obtained for a class of nonautonomous second order Hamiltonian systems with a new superquadratic condition. Furthermore, we can get the existence of homoclinic solutions as the limit of subharmonics under a stronger superquadratic condition which is still weaker than the growth conditions in the references

[en] Our aim in this paper is to study the well-posedness and the dissipativity of higher-order anisotropic conservative phase-field systems. More precisely, we prove the existence and uniqueness of solutions and the existence of the global attractor.

[en] The Bethe ansatz solutions for an open XXZ spin chain with arbitrary spin with N sites and nondiagonal boundary terms are revisited. The anisotropy parameter, for cases considered here, has values η=iπ(r/q), where r and q are positive integers with q restricted to odd integers. Numerical results are presented to support the solutions. (paper)

[en] Two types of symmetry of a generalized Zakharov-Kuznetsov equation are obtained via a direct symmetry method. By selecting suitable parameters occurring in the symmetries, we also find some symmetry reductions and new explicit solutions of the generalized Zakharov-Kuznetsov equation.

No abstract available