6533b7d0fe1ef96bd1259f8f

RESEARCH PRODUCT

Quasi-rational solutions of the NLS equation and rogue waves

Pierre Gaillard

subject

NLS equationNonlinear Sciences::Exactly Solvable and Integrable Systems[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP][ SHS.CLASS ] Humanities and Social Sciences/Classical studiesWronskians[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP][SHS.CLASS] Humanities and Social Sciences/Classical studies[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][SHS.CLASS]Humanities and Social Sciences/Classical studiesNonlinear Sciences::Pattern Formation and SolitonsNLS equation.Riemann theta functionFredholm determinants

description

We degenerate solutions of the NLS equation from the general formulation in terms of theta functions to get quasi-rational solutions of NLS equations. For this we establish a link between Fredholm determinants and Wronskians. We give solutions of the NLS equation as a quotient of two wronskian determinants. In the limit when some parameter goes to $0$, we recover Akhmediev's solutions given recently It gives a new approach to get the well known rogue waves.

yearjournalcountryeditionlanguage
2010-11-04
https://shs.hal.science/halshs-00536287v6