Benjamin-Ono-Burgers-MKdV equation for algebraic Rossby solitary waves in stratified fluids and conservation laws. (English) Zbl 1470.76024

Summary: In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.


76B25 Solitary waves for incompressible inviscid fluids
35Q53 KdV equations (Korteweg-de Vries equations)
76U65 Rossby waves
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
Full Text: DOI


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