We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term. Crank-Nicolson nonlinear-implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simu...

We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with posit...

We examine deterministic and nondeterministic state complexities of regular operations on prefixfree languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of pr...

For a many-body system of arbitrary dimension, we consider fermionic ground states non-interacting Hamiltonians invariant under $C_2$ cyclic group. The absolute difference $\Delta$ between the number occupied symmetric and anti-symmetric single-particle is an adiabatic invariant. We prove lower bounds on configurational entropy based this In band insulators, topological can be directly determin...

Abstract Symmetric operators have benefited in different fields not only mathematics but also other sciences. They appeared the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with special class meromorphically multivalent functions punctured unit disk. This study explores some its geometric properties. We conside...

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups Eτ,η(glN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.

The Schrödinger equation is one of the most basic equations in quantum mechanics. In this paper, we study convergence symmetric discretization models for nonlinear dark solitons’ motion and verify theoretical results through numerical experiments. Via second-order difference, can obtain two popular space-symmetric motion: direct-discrete model Ablowitz–Ladik model. Furthermore, applying midpoin...