（2+1）维Boiti-Leon-Pempinelli系统的相似约化、新行波解和守恒律
Similarity reductions, new traveling wave solutions, conservation laws of (2+1)- dimensional Boiti-Leon-Pempinelli system
摘要：
本文给出了（2+1）维Boiti-Leon-Pempinelli非线性偏微分方程组的精确解，该方程组描述了两个方向上传播的水波的水平速度分量的演化。我们对给定的系统进行李对称性分析，构造了涉及空间变量任意函数的一维最优子代数。利用每个最优子代数的对称约化，得到了几个新的精确解。然后通过数值模拟研究了一些精确解的物理行为，观察到了许多有趣的现象，如行波、块型孤子、扭结和反扭结型孤子、呼吸孤子、奇异扭结型孤子等。作为应用，我们通过构造势系统和附加规范约束研究了系统的非定域守恒律。
英文摘要：
In this article we obtain exact solutions of (2+1)-dimensional Boiti-Leon-Pempinelli system of nonlinear partial differential equations which describes the evolution of horizontal velocity component of water waves propagating in two directions. We perform the Lie symmetry analysis to the given system and construct one-dimensional optimal subalgebra which involves some arbitrary functions of spatial variables. Several new exact solutions are obtained by symmetry reduction using each of the optimal subalgebra. We then study the physical behavior of some exact solutions by numerical simulations and observed many interesting phenomena such as traveling waves, lump type solitons, kink and anti-kink type solitons, breather solitons, singular kink type solitons and etc. We construct several conservation laws of the system by using multipliers method. As an application, we study the nonlocal conservation laws of the system by constructing potential systems and appending gauge constraints.
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