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Zbl 1061.35142
Yin, Zhaoyang
On the Cauchy problem for an integrable equation with peakon solutions.
(English)
[J] Ill. J. Math. 47, No. 3, 649-666 (2003). ISSN 0019-2082

The non-linear family of partial differential equations, $$u_t+c_0u_x+\gamma u_{xxx}-\alpha^2 u_{txx}= (c_1u^2+c_2u_x^2+c_3uu_{xx})_x,$$ contains the Korteweg-de Vries and the Camassa-Holm equations as particular cases. These two equations are considered integrable", because for some boundary conditions they can be solved using linear methods. Another differential equation in this family with similar integrability" properties is $$u_t-u_{txx}+4uu_x= 3u_xu_{xx}+uu_{xxx}.$$ The paper under review studies the Cauchy problem for the above equation.
[Juan J. Morales-Ruiz (Barcelona)]
MSC 2000:
*35Q58 Other completely integrable PDE
37K40 Soliton theory, asymptotic behavior of solutions
35G25 Initial value problems for nonlinear higher-order PDE
35L05 Wave equation

Keywords: Cauchy problem; integrable evolution equations; Korteweg-de Vries equation; Camassa-Holm equation

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