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  • Springer  (3)
  • 1985-1989  (3)
  • 1
    Electronic Resource
    Electronic Resource
    On the continuous limit for a system of classical spins (1986)
    Springer
    Communications in mathematical physics 107 (1986), S. 431-454 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The continuum limit of a cubic latice of classical spins processing in the magnetic field created by their closest neighbours is considered. Results concerning existence, uniqueness and (for initially small spin deviation) long time behaviour, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01220998
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On the long time behaviour of a generalized KdV equation (1986)
    Springer
    Acta applicandae mathematicae 7 (1986), S. 35-47 
    Details
    ISSN: 1572-9036
    Keywords: 35Q20 ; 35B40 ; Nonlinear waves ; well posedness ; asymptotic behaviour
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the Cauchy problem for the generalized Korteweg-de Vries equation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabgkGi2oaaBaaaleaacaaIXaaabeaakiaadwhacqGHRaWkcqGH% ciITdaWgaaWcbaGaamiEaaqabaGccaGGOaGaeyOeI0IaeyOaIy7aa0% baaSqaaiaadIhaaeaacaaIYaaaaOGaaiykamaaCaaaleqabaGaeqyS% degaaOGaamyDaiabgUcaRiabgkGi2oaaBaaaleaacaWG4baabeaakm% aabmGabaWaaSaaaeaacaWG1bWaaWbaaSqabeaacqaH7oaBaaaakeaa% cqaH7oaBaaaacaGLOaGaayzkaaGaeyypa0JaaGimaaaa!56D5!\[\partial _1 u + \partial _x ( - \partial _x^2 )^\alpha u + \partial _x \left( {\frac{{u^\lambda }}{\lambda }} \right) = 0\] where α is a positive real and λ and integer larger than 1. We obtain the detailed large distance behaviour of the fundamental solution of the linear problem and show that for α≥1/2 and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabeU7aSjabg6da+iabeg7aHjabgUcaRmaalaaabaGaaG4maaqa% aiaaikdaaaGaey4kaSYaaeWaceaacqaHXoqydaahaaWcbeqaaiaaik% daaaGccqGHRaWkcaaIZaGaeqySdeMaey4kaSYaaSaaaeaacaaI1aaa% baGaaGinaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaaigdacaGGVa% GaaGOmaaaaaaa!4FF7!\[\lambda 〉 \alpha + \frac{3}{2} + \left( {\alpha ^2 + 3\alpha + \frac{5}{4}} \right)^{1/2} \], solutions of the nonlinear equation with small initial conditions are smooth in the large and asymptotic when t→±∞ to solutions of the linear problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00046976
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    Paper (German National Licenses)
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  • 3
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    On the continuous limit for a system of classical spins (1986)
    Springer
    Details
    Publication Date: 1986-09-01
    Print ISSN: 0010-3616
    Electronic ISSN: 1432-0916
    Topics: Mathematics , Physics
    Published by Springer
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