A New Example of Explode-Decay Solitary Waves in One-Dimension
A New Example of Explode-Decay Solitary Waves in One-Dimension
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DOI：
10.1143/jpsj.54.491
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发表时间：
1985-02
影响因子：
1.7
通讯作者：
A. Nakamura;R. Hirota
中科院分区：
文献类型：
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作者：
A. Nakamura;R. Hirota
我们发现了1+1维爆炸衰变孤立波的一个新例子。该方程是经典的Boussinesq方程，记为ut =（（1+ u）v-vxx）x，vt =（u +（1/2）v2）x，其中下标表示偏导数.爆炸衰减孤波解用Hermite多项式表示。得到了Backlund变换和逆散射变换的格式。我们证明了这些解与非线性薛定谔方程i <$t +<$x x-2 <$*<$x =0的有理解有关.
We have found a new example of the 1+1 dimensional explode-decay solitary waves. The equation is the classical Boussinesq equation written as u t =((1+ u ) v - v x x ) x , v t =( u +(1/2) v 2 ) x where subscripts represent partial derivatives. The explode-decay solitary wave solutions are expressed by the Hermite polynomials. Backlund transform and the inverse scattering transform scheme have been obtained. We have shown that the present solutions are related to the rational solutions of the nonlinear Schrodinger equation i ψ t +ψ x x -2ψ * ψψ=0.