Exact Solutions and Numerical Simulation of the Discrete Sawada–Kotera Equation

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

Exact solutions of the Saturable Discrete Nonlinear Schrödinger Equation

Exact solutions to a nonlinear Schrödinger lattice with a saturable nonlinearity are reported. For finite lattices we find two different standing-wave-like solutions, and for an infinite lattice we find a localized soliton-like solution. The existence requirements and stability of these solutions are discussed, and we find that our solutions are linearly stable in most cases. We also show that ...

Exact Solutions for Some Discrete Models of the Boltzmann Equation

Abs tra ct. For the simplest of the disc rete mod els of the Boltzmann equations , the Broad well model, exact solutions have been obtained by Co rnille [15.16] in the form of bisolitons. In the present paper, we build exact solutions for more co mplex mod els. 1. Introduction For t he las t twenty years, t he st udy of disc rete mo de ls of t he Bolt zm ann equat ion h as attract ed t he atten...

New exact solutions of the discrete fourth Painlevé equation

In this paper we derive a number of exact solutions of the discrete equation xn+1xn−1 + xn(xn+1 + xn−1) = −2znxn + (η − 3δ − z n)xn + μ (xn + zn + γ)(xn + zn − γ) , (1) where zn = nδ and η, δ, μ and γ are constants. In an appropriate limit (1) reduces to the fourth Painlevé (PIV) equation dw dz2 = 1 2w ( dw dz )2 + 32w 3 + 4zw + 2(z − α)w + β w , (2) where α and β are constants and (1) is commo...