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Direct and inverse problems for the dissipative Fermi-Pasta-Ulam-Tsingou (FPUT) model for a nonuniform lattice in a viscous gas medium
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DOI：10.1088/1361-6420/ae3b69.png)
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Abstract
En 中文
This study considered the determination of varying coefficients in the lattice oscillation equation. Within the framework of the Fermi-Pasta-Ulam-Tsingou model, we derived the KdV-Burgers (KdVB) equation with variable coefficients determined by the nonlinear elasticity and gas viscosity. This equation was integrated using a scale method for constant coefficients and low viscosity. In this case, solitons were used as modeling solutions. Inverse problems involve the reconstruction of coefficients from the KdVB equation integrals of mass, moments, and energy. If the variable coefficients are restored, then the distribution is considered a solution to the direct problem. In this case, we pose and solve inverse problems in piecewise constant and continuous function classes. Uniqueness theorems for inverse problems were proven and stable solution algorithms were developed based on these theorems. Several computer calculations were performed to confirm these theoretical results. The numerical results obtained were presented in the form of computer images and plots.
Keywords:
Lagrange equation
dissipative function
FPUT model
lattice dislocation
Korteweg-de Vries-Burgers equation
integrals of distribution
quasi-spectral method
Journal
I
IF:
2.1
Papers:
78
Citations:
8.4K
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