The stochastic, damped KdV equation

Herman, Russell L.

doi:10.1088/0305-4470/23/7/014

Cited by 49 publications

(27 citation statements)

References 9 publications

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“…refs. [40,41,42,43,44,45]). The characteristic feature of this method is that the perturbed nonlinear equation is linearized by expanding its solution about the unperturbed solution and the eigen functions for the operator associated with the linearized equation are found out.…”

Section: A Perturbation Approachmentioning

confidence: 99%

Perturbed soliton excitations in the DNA double helix

Daniel

Vasumathi

2007

Physica D: Nonlinear Phenomena

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We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation while taking into account the interstrand hydrogen bonding energy between bases and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and by constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillations in the open state configuration.

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Section: A Perturbation Approachmentioning

confidence: 99%

Perturbed soliton excitations in the DNA double helix

Daniel

Vasumathi

2007

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…Note that an equation of this form, but with an additional weak dissipation has been considered in [13]. Indeed, in this latter case where a dissipative term is added, such a noise may be viewed as a perturbation of the dissipation.…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%