## Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation

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**353**(2001), 191-208 Request permission

## Abstract:

In this paper we consider a generalized Kadomtsev-Petviashvili equation in the form \begin{equation*}( u_{t} + u_{xxx} + u^{p} u_{x} )_{x} = u_{yy} \quad (x, y) \in R^{2}, t \ge 0. \end{equation*} It is shown that the solutions blow up in finite time for the supercritical power of nonlinearity $p \ge 4/3$ with $p$ the ratio of an even to an odd integer. Moreover, it is shown that the solitary waves are strongly unstable if $2 < p < 4$; that is, the solutions blow up in finite time provided they start near an unstable solitary wave.## References

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## Additional Information

**Yue Liu**- Affiliation: Department of Mathematics, The University of Texas at Arlington, Arlington, Texas 76019
- Email: liu@math.uta.edu
- Received by editor(s): April 6, 1998
- Received by editor(s) in revised form: September 2, 1998
- Published electronically: June 8, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 191-208 - MSC (2000): Primary 35Q53, 35B60, 76B25
- DOI: https://doi.org/10.1090/S0002-9947-00-02465-X
- MathSciNet review: 1653363