The paper studies the dynamics of degenerate and nondegenerate bright solitons their collisions in two-component nonlinear Schrödinger equations coupled to Boussinesq equation. that have only single-hump profiles, exhibit both elastic inelastic collisions, velocities are identical two short wave (SW) components long (LW) component. single different forms: one them has double- or profiles all SW...

We obtain new local Calderón--Zygmund estimates for elliptic equations with matrix-valued weights linear as well nonlinear equations. introduce a novel log-BMO condition on the weight $\mathbb M$. In particular, we assume smallness of logarithm in BMO. This allows us to include degenerate, discontinuous weights. The assumption parameter is sharp and terms integrability exponent gradient. novelt...

Abstract In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and nonlinear subcritical growth. Under very general assumptions on the data, prove existence at least two weak solutions have different energy sign. Our treatment is based fibering method in form Nehari manifold. We point out cover both...

In standard MIMO LTI continuous-time systems S(A,B,C) the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the und...

In standard MIMO LTI continuous-time systems S(A,B,C) the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the und...

Abstract We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian of the underlying control problems/games along dual distributions agents. methods monotone, stable, and consistent, we prove convergence subsequences (i) degenerate equations in one space dimension (ii) nondegenerate arbitrary dimensions. also give...

DNA methylation at CpG dinucleotides can significantly increase the rate of cytosine-to-thymine mutations and the level of sequence divergence. Although the correlations between DNA methylation and genomic sequence evolution have been widely studied, an unaddressed yet fundamental question is how DNA methylation is associated with the conservation of individual nucleotides in different sequence...