Numerical Studies of the Regularized Long Wave Equation

概要

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The Renularized Lonn Wave (RLW) ecuuation, zttA-zt.-futt. -ttu...t=O, hassimilar properties to the Korteweg-de Vries (KdV) equation. For example, theRLW equation has a stable solitary solution and dispersive property, However,the RLW equation has been found to have only two invariants, while the KdVequation has an infinite number of invariants. The present nunaerical'sttrdies showthat the so-called recurrence property (almost-periodicity) for the KdV equationsolution does not hold in the case of the RLW equation solution. However, theenergy of the RLW solution is shared only among the lower modes of the system(no-thermalization). If the coefficient jt value is large (7?>1.0), it is found bynumerical computations that the recurrence property approximately holds. Somediscussions are made on?almost-periodicity of the RLW equation with a largevalue jt. Though the p-dependence of almost-periodicity of the RLW equation,does not become clear, we conjecture that collisions among many solitary wavesare not stable for the RLW equation.
社団法人日本物理学会の論文
1980-02-15