Kaup–Kupershmidt equation

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The Kaup–Kupershmidt equation is the nonlinear fifth-order partial differential equation

$u_t = u_{xxxxx}+10u_{xxx}u+25u_{xx}u_x+20u^2u_x = \frac16 (6u_{xxxx}+60uu_{xx}+45u_x^2+40u^3)_x.$

It is the first equation in a hierarchy of integrable equations with Lax operator

$\partial_x^3 + 2u\partial_x + u_x.$

[edit] References

Das, Ashok; and Ziemowit Popowicz (2005). "A nonlinearly dispersive fifth order integrable equation and its hierarchy" (PDF). Journal of Nonlinear Mathematical Physics 12 (1): 105–117. doi:10.2991/jnmp.2005.12.1.9.

[edit] External links

Eric W. Weisstein, Kupershmidt Equation at MathWorld.

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Categories: Mathematical analysis stubs | Partial differential equations

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