Related papers: Homotopy solution to non-linear evolution for heav…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
We apply a non-linear statistical method in turbulence to the cosmological perturbation theory and derive a closed set of evolution equations for matter power spectra. The resultant closure equations consistently recover the one-loop…
We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the…
In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
Using standard calculus, explicit formulas for one-, two- and three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…
We prove existence and uniqueness results for (mild) solutions to some non-linear parabolic evolution equations with a rough forcing term. Our method of proof relies on a careful exploitation of the interplay between the spatial and time…
We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves…
We present a new numerical scheme to treat the non-linear evolution of cosmological power spectra. Governing equations for matter power spectra have been previously derived by a non-perturbative technique with closure approximation.…
In this work we study the solvability of the Cauchy Problem for a quasilinear degenerate high-order parabolic equation \begin{equation*} \left\{ \begin{tabular}{lcl} $u_t=(-1)^{m-1}\nabla\cdot(f^n(|u|)\nabla\Delta^{m-1}u)$ & &in…
We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.
We analytically solve the full next-to-leading logarithmic Balitsky-Kovchegov equation in the saturation regime, which includes corrections from quark and gluon loops, and large double transverse logarithms. The analytic result for the…
This paper features and elaborates recent developments and modifications in asymptotic techniques in solving differential equation in non linear dynamics. These methods are proved to be powerful to solve weakly as well as strongly non…
We present a systematic search method for finding Hirota bilinear systems of nonlinear evolution equations, with emphasis on the nonlinear Schr\"odinger equation (NLSE). Using a known exact solution, couplings between the different terms of…
We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…
We derive two coupled non-linear evolution equations corresponding to the truncation of the Balitsky infinite hierarchy of saturation equations after inclusion of dipole-dipole correlations, i.e. one step beyond the Balitsky-Kovchegov (BK)…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…