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arXiv · 2608.23126

Non-Local Energy Dissipation and Topological Obstructions in the Second-Order Positive Modified Burgers' Equation

Prasanta Chatterjee·Suman Pal
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Abstract

We study the higher-order flows of the modified Burgers' equation generated by its standard recursion operator. In particular, we show that the second-order positive flow takes the form of a non-local integro-differential equation. After reducing the equation to a traveling-wave form, we investigate its asymptotic energy behavior. The resulting analysis shows that the non-local energy flux prevents the formation of both topological kink and bell-shaped solitary waves. We show that the non-local dissipation permanently breaks the asymptotic equilibrium between nonlinear convection and linear dispersion, forcing an irreversible energy imbalance. Our analysis shows that the solitary waves are unstable. The non-local term causes continuous energy loss through radiation. As a result, the traveling wave cannot keep a stable and symmetric shape.

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Prasanta Chatterjee, Suman Pal. 2026-08-24. Non-Local Energy Dissipation and Topological Obstructions in the Second-Order Positive Modified Burgers' Equation. https://arxiv.org/abs/2608.23126

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