Shock waves in the modified Korteweg-de Vries-Burgers equation

DOI10.1007/BF01869099zbMath0821.35119MaRDI QIDQ1345445

Ramil' F. Bikbaev

Publication date: 3 October 1995

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

instabilityattractorshock wavesviscous regularization

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05)

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Cites Work

• Unnamed Item
• Multiresolution-information analysis for images
• Exact solutions to the Korteweg-de Vries-Burgers equation
• Geometry of the modulational instability. III: Homoclinic orbits for the periodic sine-Gordon equation
• Idempotent analysis as a tool of control theory and optimal synthesis. I
• Solitons of the nonlinear Schrödinger equation generated by the continuum
• Diffraction in a nonlinear defocusing medium
• Influence of viscosity on the structure of shock waves in the MKdV model
• Example of shock waves in unstable media: The focusing nonlinear Schrödinger equation
• The small dispersion limit of the Korteweg-de Vries equation. III
• The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
• Formation of shocklike modified Korteweg–de Vries solitons: Application to double layers
• On dispersive difference schemes. I
• The hyperbolic nature of the zero dispersion Kdv limit
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• THE FUNCTIONAL REPRESENTATION OF THE UNIFORM COMPLETION OF THE MAXIMAL AND OF THE COUNTABLY DENSE MODULE OF FRACTIONS OF THE MODULE OF CONTINUOUS FUNCTIONS
• Initial boundary value problem for the nonlinear Schrodinger equation
• The toda shock problem
• Dispersive Regularization of the Whitham Equation for the Toda Lattice
• On the excitation of edge waves on beaches
• Soliton generation for initial-boundary-value problems