Blow up and instability of solitary wave solutions to a generalized Kadomtsev-Petviashvili equation and two-dimensional Benjamin-Ono equations

被引:5
作者
Chen, Jianqing [1 ,2 ]
Guo, Boling [2 ]
Han, Yongqian [2 ]
机构
[1] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350007, Peoples R China
[2] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2008年 / 464卷 / 2089期
关键词
Kadomtsev-Petviashvili equation; Benjamin-Ono equations; blow-up solutions; strong instability of solitary waves;
D O I
10.1098/rspa.2007.0013
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Let p >= 2 with p being the ratio of an even to an odd integer. For the generalized Kadomtsev Petviashvili equation, coupled with Benjamin Ono equations, in the form (u(t) + u(xxx) +beta Hu(xx) +u(p)u(x))(x) = u(yy), (x, y)is an element of R-2, t >= 0, it is proved that the solutions blow up infinite time even for those initial data with positive energy. As a by-product, it is proved that for all c >(beta/2) , the solitary waves phi(x-ct, y); are strongly unstable if 2 <= p < 4. This result, even in a special case beta=0, improves a previous work by Liu ( Liu 2001 Trans. AMS 353, 191 208) where the instability of solitary waves was proved only in the case of 2 < p < 4.
引用
收藏
页码:49 / 64
页数:16
相关论文
共 18 条
[1]  
Ablowitz M J, 1991, SOLITONS NONLINEAR E, V149
[2]  
Ambrosetti A, 2003, DISCRETE CONT DYN-A, V9, P55
[3]  
BERESTYCKI H, 1981, CR ACAD SCI I-MATH, V293, P489
[4]  
Besov O V., 1978, Integral Representations of Functions and Imbedding Theorems, Vols. 1
[5]   A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].
BREZIS, H ;
LIEB, E .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490
[6]  
CHEN J, UNPUB BLOW INSTABILI
[7]   Solitary waves of generalized Kadomtsev-Petviashvili equations [J].
deBouard, A ;
Saut, JC .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02) :211-236
[8]  
GUO B, 1992, J PART DIFFER EQNS, V5, P50
[9]  
Guo BL, 1996, P ROY SOC A-MATH PHY, V452, P1585
[10]  
GUO BL, 1992, J PART DIFF EQ, V5, P37