6533b86cfe1ef96bd12c8be4

RESEARCH PRODUCT

Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions

Caroline Kalla

subject

Statistics and ProbabilityBreatherMathematics::Analysis of PDEsGeneral Physics and AstronomyFOS: Physical sciences01 natural sciences010305 fluids & plasmasSchrödinger equationsymbols.namesakeMathematics - Analysis of PDEsSimple (abstract algebra)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesFOS: MathematicsElementary function[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsMathematical physicsPhysics[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Statistical and Nonlinear PhysicsLimitingMathematical Physics (math-ph)Mathematics::Spectral TheoryNonlinear systemNonlinear Sciences::Exactly Solvable and Integrable SystemsModeling and SimulationsymbolsAnalysis of PDEs (math.AP)

description

We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schr\"odinger equations.

yearjournalcountryeditionlanguage
2011-06-03
https://hal.science/hal-00597964