A Recurrence Formula of Solutions for Burgers Equations
Hongling Su, Mingling Wang, Mengzhao Qin
TL;DR
This paper develops a recurrence formula for solutions of Burgers equations using a Backlund transformation and the homogeneous balance method, simplifying the problem to the heat equation and enabling solution generation.
Contribution
It introduces a novel recurrence formula for Burgers equations derived via a Backlund transformation and the homogeneous balance method, connecting solutions to the heat equation.
Findings
Derived a Backlund transformation for Burgers equations.
Established a recurrence formula for solutions.
Reduced Burgers equations to heat equation solutions.
Abstract
A Backlund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the initial problem of the Burgers equations.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Numerical methods for differential equations