The benefit of finding particular exact and asymptotic solutions of non-integrable non-linear partial differential equations is considered. It is shown how explicit analytical solutions predict important features of the waves behavior even outside their formal applicability. In particular, an arbitrary initial pulse splits in a numerical solution into the train of localized waves each described...

In this paper, we present an analytical double-series solution for the time-dependent asymmetric heat conduction in a multilayer annulus. In general, analytical solutions in multidimensional Cartesian or cylindrical r , z coordinates suffer from existence of imaginary eigenvalues and thus may lead to numerical difficulties in computing analytical solution. In contrast, the proposed analytical s...

In this paper, two analytic solutions for the valuation of European-style Parisian and Par. asian options under the Black-Scholes framework are, respectively, presented. A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one. Compared with some previ...

We present a method to derive implicit solvent models of electrolyte solutions from all-atom descriptions; providing analytical expressions of the thermodynamic and structural properties of the ions consistent with the underlying explicit solvent representation. Effective potentials between ions in solution are calculated to perform perturbation theory calculations, in order to derive the best ...

This paper provides explicit analytical expressions for displacement and stress fields in a multilayered composite cylinder with cylindrically orthotropic layers subjected to homogeneous boundary conditions. The solutions are derived in the assumption of perfect bonding between layers. The components of displacement, strain and stress are expressed in terms of the integration constants found fr...

We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae fo...

In this paper, the (2+1)-dimensional q-deformed Sinh-Gordon model has been investigated via (G?G,1G)-expansion and Sine-Gordon-expansion methods. These techniques successfully retrieve trigonometric as well hyperbolic solutions, along necessary restricted conditions applied on parameters. addition to these dark solitons complexiton solutions have also obtained. The proposed equation expands pos...

In this paper, we use two approaches to solve the Perspective-Three-Point (P3P) problem: the algebraic approach and the geometric approach. In the algebraic approach, we use Wu-Ritt’s zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. We also give a complete ...