Abundant optical soliton solutions for an integrable (2+1)-dimensional nonlinear conformable Schrödinger system

Abstract The analytical solutions of the integrable generalized ( 2 + 1 ) -dimensional nonlinear conformable Schrodinger (NLCS) system of equations was explored in this paper with the aid of three novel techniques which consist of ( G ′ / G ) -expansion method, generalized Riccati equation mapping method and the Kudryashov method in the conformable sense. We have discovered a new and more general variety of exact traveling wave solutions by using the proposed methods with a variety of soliton solutions of several structures. With several plots illustrating the behavior of dynamic shapes of the solutions, the findings are highly applicable and detailed the physical dynamic of the considered nonlinear system

Algebraic models for a second-order modal logic

We propose a predicative modal logic of the second order for expressing properties of the evolution of software systems. Each state of a system is specified as a unary algebra, and our logics allows to formalize the problem of verifying the properties of system evolutions as the checking of the truth of suitable formulas. The level of abstraction guaranteed by the algebraic presentation of system states allows the unification of many proposals in the literature, at the same time obtaining a greater level of expressiveness in terms of system representability. Due to a different handling of the so-called “trans-world identity”, we consider two alternative semantics for our logic: a “Kripke-like” model and a “Counterpart-like” one. Furthermore, we instantiate our proposal by considering unary algebras representing graphs, thus showing the applicability of our approach to the graph transformation framework

Quantum trajectories for a class of continuous matrix product input states

We introduce a new class of continuous matrix product (CMP) states and establish the stochastic master equations (quantum filters) for an arbitrary quantum system probed by a bosonic input field in this class of states. We show that this class of CMP states arise naturally as outputs of a Markovian model, and that input fields in these states lead to master and filtering (quantum trajectory) equations which are matrix-valued. Furthermore, it is shown that this class of continuous matrix product states include the (continuous-mode) single photon and time-ordered multi-photon states.Comment: 17 pages, 2 figure