A Gardner-type equation: bore propagation

DOI10.1007/s00574-024-00424-5MaRDI QIDQ6656093

Marcia Scialom, Mahendra Panthee, Jerry L. Bona, Hongqiu Chen

Publication date: 2 January 2025

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

zbMATH Keywords

Gardner equationbore propagationplasma physics modelslong-wave modelsunidirectional water-wave models

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Cites Work

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• Models for propagation of bores. I: Two dimensional theory
• A derivation of Gardner's equation
• Models for internal waves in deep water
• KdV and BO equations with bore-like data
• Propagation of long-crested water waves. II. Bore propagation
• The Korteweg–deVries Equation: A Survey of Results
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• Model equations for long waves in nonlinear dispersive systems

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