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arXiv · 2607.01348

Sharp Upper Bound for Amplitudes of Finite-Gap Solutions of the Modified Korteweg-de Vries Equation

Otis C. Wright
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Abstract

A direct proof based on commuting finite-dimensional flows and local polynomial invariants is given for a sharp upper bound on the amplitudes of finite-gap solutions of the modified Korteweg-de Vries (mKdV) equation. The maximal amplitude is the sum of the imaginary parts of the upper-half-plane square roots of the roots of the invariant polynomial of the finite-gap solution of the focusing mKdV equation. An analogous formula is established for a bounded class of solutions of the defocusing mKdV equation. The upper bounds are sharp and are explicitly attained by suitable initial data.

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Otis C. Wright. 2026-07-01. Sharp Upper Bound for Amplitudes of Finite-Gap Solutions of the Modified Korteweg-de Vries Equation. https://arxiv.org/abs/2607.01348

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