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Search: MSC category 35Q51 ( Soliton-like equations [See also 37K40] )

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1. CJM 2011 (vol 63 pp. 1201)

Abou Salem, Walid K. ; Sulem, Catherine
Resonant Tunneling of Fast Solitons through Large Potential Barriers
We rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schrödinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).

Keywords:nonlinear Schroedinger equations, external potential, solitary waves, long time behavior, resonant tunneling
Categories:37K40, 35Q55, 35Q51

2. CJM 1998 (vol 50 pp. 1119)

Anand, Christopher Kumar
Ward's solitons II: exact solutions
In a previous paper, we gave a correspondence between certain exact solutions to a \((2+1)\)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions. Dans un article pr\'{e}c\'{e}dent, nous avons d\'{e}montr\'{e} que les solutions d'un mod\`{e}le chiral int\'{e}grable en dimension \( (2+1) \) correspondent aux fibr\'{e}s vectoriels holomorphes sur une surface compacte. Ici, nous employons la g\'{e}om\'{e}trie alg\'{e}brique dans une construction explicite des solutions. Nous donnons une formule matricielle et illustrons avec trois exemples la signification des invariants alg\'{e}briques pour le comportement physique des solutions.

Keywords:integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map

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