First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping
Abbreviated Journal Title
J. Phys. A-Math. Theor.
KORTEWEG-DEVRIES EQUATION; QUANTUM-FIELD THEORY; DE-VRIES EQUATION; LOCAL GAUGE-THEORIES; DELTA-EXPANSION; ASYMPTOTIC STABILITY; NONPERTURBATIVE CALCULATION; WAVES; Physics, Multidisciplinary; Physics, Mathematical
We discuss an application of the delta-expansion method to the soliton perturbation theory for a generalized KdV model with stochastic forcing and damping. We find that the delta-expansion method is a perturbation technique which allows one to retain a more representative linearization for a nonlinear differential equation (than comparable methods of perturbation, such as those relying on small parameters). Indeed, one primary benefit of the method is that it tends to provide much more reasonable solutions with relatively few terms (compared to standard perturbation methods) due to the more accurate linearization. We show that the method allows one to obtain first-order perturbations in which the stochastic and nonlinear contributions separate, allowing one to study each influence independently (at least, to first order). We then apply the delta-expansion method to the study of a stochastic generalized KdV model, and we show that this procedure gives a natural extension to the perturbation theory for the traditional KdV model. The actual method of computation is outlined and may be applied to a variety of generalized KdV models.
Journal of Physics a-Mathematical and Theoretical
"First-order soliton perturbation theory for a generalized KdV model with stochastic forcing and damping" (2011). Faculty Bibliography 2010s. 2027.