Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Father Abbey's Will Cambridge, Dec. 1731. Some time since..., [ca. 1780]

Goodspeed 5, Ford 615.

Father Abbey's Will, Cambridge, Dec. 1731. Some time since..., [ca. 1780]

Goodspeed 6.

Photostat copy of Old Timothy Jobson. TO my dear Wife, my Joy and Life, [ca. 1780]

Goodspeed 4, Ford 618.

Photostat copy of Father Abbey's Will. To which is now added, A Letter of Courtship to his virtuous..., [ca. 1780]

Goodspeed 7, Ford 612.

Vote of the Selectmen of Boston respecting Clarke's children, 1780 August 30

One-page handwritten copy of the vote of the Boston Selectmen responding to Croswell's complaint, as usher of the South Grammar School of Boston, against a parent.

Indenture, 1780

Handwritten indenture for a Boston property between James Tate, the agent for the estate of Edward Keithley, and Andrew Croswell.

Pennsylvanian invertebrates of the Mazon Creek Area, Illinois: the morphology and affinities of Tullimonstrum / Ralph Gordon Johnson -- and Eugene S. Richardson, Jr. --

v.12:no.8(1969)

Letter from Francis Dana to Samuel Langdon, 1780 January 19

This one-page letter from Harvard alumnus Francis Dana (1743-1811; Harvard AB 1762), in Bilbao, Spain, to Harvard President Samuel Langdon concerns the donation of a Spanish book by Dana to the College Library.

Book receipt of John Mellen and William Bentley, 1780 June 16

This half-page slip contains receipts for two Harvard College Library books received by Harvard College Tutors John Mellen (1752-1828; Harvard AB 1770) and William Bentley (1759-1819; Harvard AB 1777).

Petition of John Wyeth to the Harvard Corporation, 1780 August 23

In this brief petition of John Wyeth to the Harvard Corporation, he requests the ability to borrow books from the "Publick Library" of the College.

Bill from Phillips Payson to Harvard College, [1780 August]

This undated bill was rendered to the College by Phillips Payson (died 1809; Harvard AB 1778) for work done in the College Library equaling £720. The document was originally housed in a folder with the note, "This was from the old trunk."

Letter and account from Phillips Payson to Harvard College, 1780 September 11

These two documents consist of an account of services done by Phillips Payson (1809; Harvard AB 1778) for the College Library and a brief letter of enclosure.