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Homoclinic orbits for a modified KdV equation

Monday 22nd October 2001 - 15:00 to 16:00
INI Seminar Room 1
We study the homoclinic structure of modified Korteweg--de Vries equation under dissipative perturbations. The homoclinic orbits are constructed through the Backlund transformation of mKdV equation. For external parameters on a codimension 1 submanifold, the persistence of homoclinic solutions to periodic traveling waves is established through an argument which combines Mel'nikov method and the dynamics of the finite dimensional reduced system on the plane of periodic traveling waves.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons