On Some Classes of mKdV Periodic Solutions

Details On Some Classes of mKdV Periodic Solutions On Some Classes of mKdV Periodic Solutions

2004-10-21

arxiv.org/abs/nlin/0410047v1

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 3 figures, to appear in J. Phys. A

Scientific paper

10.1088/0305-4470/37/45/014

We obtain exact periodic solutions of the positive and negative modified Kortweg-de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation.

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