Self-similar asymptotics in the decay problem for the Volterra lattice with zero boundary condition

2026/06/11 by V. E. Adler, B. I. Suleimanov · 1 voice
Physics and Astronomy · #nlin.PS #math-ph

paper · pdf

Abstract

The article is devoted to the problem of decay of initial stationary state for the Volterra lattice with zero boundary condition. We show that this process is asymptotically self-similar and calculate the propagation velocity of the decay wave, the leading terms of the asymptotics and corrections, in the main and transition sectors of the wave.

Citations

• Asymptotic integrability and its consequences
• Asymptotic integrability of nonlinear wave equations
• KdV equation beyond standard assumptions on initial data
• Rational Solutions of the Painlevé-II Equation Revisited
• Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data
• Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation
• Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit
• Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
• The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation
• On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour

Discussions

• V. E. Adler, B. I. Suleimanov: Self-similar asymptotics in the decay problem for the Volterra lattice with zero boundary condition https://arxiv.org/abs/2606.13137 https://arxiv.org/pdf/2606.13137 htt [bsky, 0 points, 0 comments]

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