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- W2023677513 abstract "Generalized Korteweg-de Vries equations with higher nonlinearities are considered. First, it is shown by simple arguments that a collapse could occur if the nonlinearity is large enough. It is also proved that for some parameters no collapse can take place. The proof of the conjecture that in the complementary parameter region higher nonlinear Korteweg-de Vries equations have a focusing singularity is, however, far from being complete. Therefore, in the second part of the paper, the variation of action method, with a collective coordinate ansatz, is used to demonstrate collapse for power-law nonlinearities (qpqx) at and above the critical exponent p = 4. It is shown that the time dependence of the focusing amplitude is of the form (tc − t)−1(p + 2) where tc is the collapse time." @default.
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- W2023677513 date "1989-12-01" @default.
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- W2023677513 title "Collapsing states of generalized Korteweg-de Vries equations" @default.
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- W2023677513 doi "https://doi.org/10.1016/0167-2789(89)90066-3" @default.
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