Fifth-order Korteweg–de Vries equation

A fifth-order Korteweg–de Vries (KdV) equation is a nonlinear partial differential equation in 1+1 dimensions related to the Korteweg–de Vries equation.[1] Fifth order KdV equations may be used to model dispersive phenomena such as plasma waves when the third-order contributions are small. The term may refer to equations of the form

where is a smooth function and and are real with . Unlike the KdV system, it is not integrable. It admits a great variety of soliton solutions.[2]

References

  1. Andrei D. Polyanin, Valentin F. Zaitsev, HANDBOOK of NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p 1034, CRC PRESS
  2. "Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework" (PDF). Retrieved 8 May 2015.


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