A fast adaptive vortex method for patches of constant vorticity in two dimensions
Journal of Computational Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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In this paper we present some numerical results about the existence of a new family of solutions of the geometric mKdV equation. This equation is characterized by the fact that the curvature evolves according to the focusing mKdV equation. The new type of solutions are similar to the breathers found by M. Wadati in 1973. We exhibit curves with and without self-intersections, and also some examples of initially simple closed curves that have self-crossings at later times.