Investigation of zero-frequency solutions to the pion dispersion equation

Spectra of Short Pulse Solutions of the Cubic–Quintic Complex Ginzburg–Landau Equation near Zero Dispersion

We describe a computational method to compute spectra and slowly decaying eigenfunctions of linearizations of the cubic–quintic complex Ginzburg– Landau equation about numerically determined stationary solutions. We compare the results of the method to a formula for an edge bifurcation obtained using the small dissipation perturbation theory of Kapitula and Sandstede. This comparison highlights...

Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1leq qleq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equa...

Numerical Solutions of the Fractional Advection- Dispersion Equation

In this paper we have used the homotopy analysis method (HAM) to obtain solution of space-time fractional advectiondispersion equation. The fractional derivative is described in the Caputo sense. Some illustrative examples have been presented. The obtained results using homotopy analysis method demonstrate the reliability and efficiency of the proposed algorithm.

HYPERGEOMETRIC SOLUTIONS OF THE qKZ EQUATION AT LEVEL ZERO

We discuss relations between different integral formulae for solutions of the quantized Knizhnik-Zamolodchikov (qKZ) equation at level zero in the Uq(sl2) case for |q | < 1 . Smirnov type formulae of M. Jimbo et al. are derived from the general approach of A.Varchenko and the author. The consideration is parallel to the qKZ equation in the rational sl2 case done by A.Nakayashiki, S. Pakuliak an...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION