Stability of discontinuity structures described by a generalized KdV-Burgers equation

DOI10.1134/S0965542516020056zbMath1346.35178MaRDI QIDQ2630010

A. P. Chugainova, V. A. Shargatov

Publication date: 8 July 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

generalized KdV-Burgers equationspecial discontinuitiesspectral (linear) stability of stationary solutions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (16)

Structures of non-classical discontinuities in solutions of hyperbolic systems of equations ⋮ On nonlinear superposition of the KdV-Burgers shock waves and the behavior of solitons in a layered medium ⋮ Long nonlinear waves in anisotropic cylinders ⋮ On the instability of monotone traveling-wave solutions for a generalized Korteweg-de Vries-Burgers equation ⋮ Boundary value problem for the KdV-Burgers equation in a quarter plane ⋮ The effect of small-scale processes in the structure of discontinuities on the solution of the Riemann problem ⋮ Analytical description of the structure of special discontinuities described by a generalized KdV-Burgers equation ⋮ Hamiltonian operators in differential algebras ⋮ Stability of shock wave structures in nonlinear elastic media ⋮ Periodic boundary conditions for KdV-Burgers equation on an interval ⋮ Uniqueness of self-similar solutions to the Riemann problem for the Hopf equation with complex nonlinearity ⋮ Spectral stability theory of heteroclinic solutions to the Korteweg-de Vries-Burgers equation with an arbitrary potential ⋮ Shock waves in anisotropic cylinders ⋮ Flow structure behind a shock wave in a channel with periodically arranged obstacles ⋮ Stability analysis of traveling wave solutions of a generalized Korteweg-de Vries-Burgers equation with variable dissipation parameter ⋮ Longitudinal and torsional shock waves in anisotropic elastic cylinders

Cites Work

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• Spectral stability of special discontinuities
• Oscillatory instability of traveling waves for a KdV-Burgers equation
• Stability of nonstationary solutions of the generalized KdV-Burgers equation
• Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation
• Classical and non-classical discontinuities in solutions of equations of non-linear elasticity theory
• Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation

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