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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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