Benjamin–Ono equation

In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that

describes one-dimensional internal waves in deep water.

It was introduced by {{harvtxt|Benjamin|1967}} and {{harvtxt|Ono|1975}}.

The Benjamin–Ono equation is

:u_t+uu_x+Hu_{xx}=0

where H is the Hilbert transform.

It possesses infinitely many conserved densities and symmetries; thus it is a completely integrable system.A two-parameter Miura transformation of the Benjamin-Ono equation,

T.L. Bock, M.D. Kruskal, Physics Letters A, Volume 74, Issues 3–4, 12 November 1979, Pages 173-176.

See also

References

{{reflist}}

Sources

  • {{citation

| last = Benjamin | first = T. Brooke | authorlink = Brooke Benjamin

| doi = 10.1017/s002211206700103x

| issue = 3

| journal = Journal of Fluid Mechanics

| page = 559

| title = Internal waves of permanent form in fluids of great depth

| volume = 29

| year = 1967| bibcode = 1967JFM....29..559B | s2cid = 123065419 }}

  • {{citation

| last = Ono | first = Hiroaki

| doi = 10.1143/JPSJ.39.1082

| issue = 4

| journal = Journal of the Physical Society of Japan

| mr = 0398275

| pages = 1082–1091

| title = Algebraic solitary waves in stratified fluids

| volume = 39

| year = 1975| bibcode = 1975JPSJ...39.1082O

}}