辅助方程法求变系数KdV方程组的精确解

The exact solutions to coupled KdV equations with variable coefficients by auxiliary equation method

求解变系数非线性发展方程是数学、物理、力学等诸多自然科学研究的重要领域。文中创建辅助方程法,可求多种常系数与变系数非线性发展方程的精确解。以变系数非线性KdV方程组为例,在仅要求变系数可积的情形下,获得了一系列新的精确解。

Solving nonlinear evolution equations with variable coefficients is an important field in mathematics,physics,mechanics and many other fields in natural sciences.An auxiliary equation method is proposed,which can be used to solve many kinds of nonlinear evolution equations with constant and variable coefficients.Taking the coupled KdV equations with variable coefficients as an example,a series of new exact solutions are obtained under the condition that only variable coefficients are required to be integrals.