The inverse scattering problem on half-axis, in other words, in the spherically symmetric case, consists of finding the unknown potential from a suitable class from the scattering data S. The other problem of practical interest is to find this potential from the spectral data dρ(λ). In the literature there are recovery procedures for finding the potential from the spectral or from the scatterin...

A numerical method for integrating the equations describing a dynamically coupled system made of a fluid and cosmic-rays is developed. In smooth flows the effect of CR pressure is accounted for by modification of the characteristic equations and the energy exchange between cosmic-rays and the fluid, due to diffusive processes in configuration and momentum space, is modeled with a flux conservin...

An extension of the Colombo phase transition model is proposed. The congestion phase is described by a two-dimensional zone defined around an equilibrium flux known as the classical fundamental diagram. General criteria to build such a set-valued fundamental diagram are enumerated, and instantiated on several equilibrium fluxes with different concavity properties. The solution of the Riemann pr...

In this paper, we extend the second and third order classical central schemes for the hyperbolic conservation laws to solve the modified Buckley-Leverett (MBL) equation which is of pseudo-parabolic type. The MBL equation describes two-phase flow in porous media, and it differs from the classical Buckley-Leverett (BL) equation by including a balanced diffusive-dispersive combination. The classic...

In this paper we study the Cauchy–Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the ∂̄-Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the ∂̄-Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in comple...

The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schrödinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed analysis of the adiabatic approximation to perturbation-induced evolution of the soliton parameters is given. The linear perturbation and the Raman gain are cons...

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired ob...

In this paper, we study the inverse scattering transform for coupled modified Korteweg-de Vries (cmKdV) equation with nonzero boundary conditions (NZBCs) at infinity. order to deal direct and problems, a suitable uniformization variable is given on complex plane by transforming two-sheeted Riemann surface. problem, discuss analyticity, three symmetries asymptotic behaviors of Jost functions, ma...