非线性弦振动方程的相似约化

Similarity Reductions for the Nonlinear Vibrating String Equation

应用经典无穷小Lie群方法和CK直接方法得到了非线性弦振动方程的新的相似约化和新的精确解。应用经典Lie群方法将非线性弦振动方程约化成了第三类和第四类椭圆方程,同时得到了非线性弦振动方程的显式类孤立波解。进而,应用不涉及群论的CK直接方法得到了非线性弦振动方程的更为一般的相似约化。

New explicit solutions and new similarity reductions are presented for the nonlinear vibrating string equation, by means of both the classical Lie group method of infinitesimal transformation and the CK direct method. Using the classical Lie group method, the nonlinear vibrating string equation can be reduced to the third and fourth type elliptic equations, and the new explicit soliton-like solution is obtained at the same time. The more general similarity reductions are obtained by the CK direct method, this method does not require the Lie group theoretic techniques.