Breather lattice and its stabilization for the modified Korteweg-de Vries equation

Abstract

We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However, such multi-breather structures can be stabilized through the concurrent application of ac driving and viscous damping terms.

arXiv comment6 pages, 3 figures, Phys. Rev. E (in press)

References in corpus (3)

• Discrete Breathers
• A Kink Soliton Characterizing Traffic Congestion
• Spatial chaos in weakly dispersive and viscous media: a nonperturbative theory of the driven KdV-Burgers equation

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• On the nonlinear stability of mKdV breathers
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• The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
• Dark discrete breather modes in monoaxial chiral helimagnet with easy-plane anisotropy
• Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations
• On the variational structure of breather solutions
• A systematic construction of parity-time ($\mathcal{P}\mathcal{T}$)-symmetric and non-$\mathcal{P}\mathcal{T}$-symmetric complex potentials from the solutions of various real nonlinear evolution equations
• Nonlinear stability of higher order mKdV breathers