Stochastic Korteweg-de Vries Equation with and without Damping

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  • Wadati Miki
    Institute of Physics, College of Arts and Sciences, University of Tokyo
  • Akutsu Yasuhiro
    Institute of Physics, College of Arts and Sciences, University of Tokyo

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  • Stochastic Korteweg de Vries Equation w

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Introducing the Korteweg-de Vries equation with a damping term and an external force, the behaviors of solitons under the Gaussian white noise is studied. In the non-damping case, a height and a width of the soliton are proportional to t−3⁄2 and t3⁄2 respectively, for large t. The asymptotic form of the multi-soliton is also discussed. In the damping case, it is found that a width of the soliton is much narrow while a height is much small as compared with the non-damping case. A new idea for the analysis of inhomogeneous soliton equation is suggested.

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