Rational solitons of wave resonant-interaction models.
Rational solitons of wave resonant-interaction models.
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DOI：
10.1103/physreve.88.052914
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
A. Degasperis;S. Lombardo
中科院分区：
文献类型：
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作者：
A. Degasperis;S. Lombardo
1+1维中两个或多个波的共振相互作用的可积模型在几个领域具有应用价值。这里我们考虑一个三波耦合方程组，它包括作为特殊情况的矢量非线性薛定谔方程和描述三波共振相互作用的方程。孤子解的Darboux-Dressing构造适用于解对坐标具有有理或混合有理指数依赖的条件。我们的代数结构依赖于使用幂零矩阵及其约旦形式。我们系统地搜索所有有界理性（混合理性指数）的解决方案，并找到一个广泛的家庭，这样的解决方案的三波共振相互作用方程。
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations.