Yajima, Nobuo On a growing mode of the Boussinesq equation. (English) Zbl 1098.76521 Prog. Theor. Phys. 69, No. 2, 678-680 (1983). Summary: From the summary: The nonlinear evolution of linearly unstable solutions in the Boussinesq system is studied by R. Hirota’s method [J. Math. Phys. 14, 810–814 (1973; Zbl 0261.76008)]. The result shows the peculiar property that the unstable solution neither grows unboundedly nor falls into a saturation level, but attains the maximum amplitude at a certain time, and thereafter damps. Cited in 7 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35Q53 KdV equations (Korteweg-de Vries equations) Citations:Zbl 0261.76008 PDFBibTeX XMLCite \textit{N. Yajima}, Prog. Theor. Phys. 69, No. 2, 678--680 (1983; Zbl 1098.76521) Full Text: DOI