The main physical result of this paper are exact analytical solutions of the heavenly equation, of importance in the general theory of relativity. These solutions are not invariant under any subgroup of the symmetry group of the equation. The main mathematical result is a new method of obtaining noninvariant solutions of partial differential equations with infinite dimensional symmetry groups. ...

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces e cient algorithms exist even for almost degenerate surfaces. This allows the numeri...

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By...

In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigen...

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

Consider the differential inclusion Du ∈ E in R. We exhibit an explicit solution that we call fundamental. It turns out to be also a viscosity solution, when properly defining this notion. Finally we consider a Dirichlet problem associated to the differential inclusion and we give an iterative procedure for finding a solution.

• Analytical solution to nonlinear routing with arbitrary power-law storage function is presented. Constant inflow produces incomplete beta outflow. Explicit Lambert-W outflow for linear storage-depth orifice outlet provided. A new analytical a general The resulting implicit solution, expressed in terms of the function, valid hydrographs that may be represented by series pulses widths. thus ext...

Abstract We use the monodromy method to investigate asymptotic quasinormal modes of regular black holes based on explicit Stokes portraits. find that, for with spherical symmetry and a single shape function, analytical forms frequency spectrum are not universal do depend multipole number but presence complex singularities trajectory solutions along lines.