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Zbl 1182.35064
Gómez, Cesar A.; Salas, Alvaro H.
Exact solutions for a new integrable system (KDV6). (English)
[J] J. Math. Sci. Adv. Appl. 1, No. 2, 401-413 (2008). ISSN 0974-5750

Summary: We obtain exact solutions for the new integrable system $$u_t-6uu_x- u_{xxx}+ w_x=0, \qquad w_{xxx}+ 4uw_x+ 2u_xw=0,$$ which has been derived from the new integrable sixth-order KdV equation (KdV6) $(\partial_x^3+ 8u_x\partial_x+ 4u_{xx})(u_t+u_{xxx}+6u_x^2)=0$. Using the generalized tanh-coth method, periodic and soliton solutions are formally derived for it.

MSC 2000:: *35C05 Solutions of PDE in closed form
35B10 Periodic solutions of PDE
35G50
35C08
35Q53 KdV-like equations

Keywords: generalized tanh-coth method

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Zentralblatt MATH Berlin [Germany]