# On some classes of mKdV periodic solutions

@article{Kevrekidis2004OnSC, title={On some classes of mKdV periodic solutions}, author={Panayotis G. Kevrekidis and Avinash Khare and Avadh B Saxena and G. Herring}, journal={Journal of Physics A}, year={2004}, volume={37}, pages={10959-10965} }

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…

## 31 Citations

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- 2016

Abstract
We present closed form periodic solutions of the integrable modified Korteweg-de Vries
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doubly-periodic…

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The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained.…

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We present closed form breather solutions of the integrable modified Korteweg-de Vries equation (mKdV). By using a Darboux transformation, we derive firstand second-order doubly-periodic lattice-like…

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Breather Lattice Solutions to Negative mKdV Equation

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In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic…

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