【摘要】 对最近提出的G’/G展开法进行了进一步扩展,利用扩展后的方法研究了描述沿着y轴传播的Riemann波和沿着x轴传播的长波的(2+1)维相互作用的重要模型—(2+1)维破裂孤子方程组,得到了该方程组的3类涉及任意参数的新型精确行波解,当这些参数取特殊值时,可得它的钟状孤立波解、扭状孤立波解以及三角函数解等.该精确解的发现对实际模型的物质运动规律和物理机制的深入探索有着积极的作用.研究结果表明,该方法是探讨非线性偏微分方程精确解的一个十分有效的数学工具.更多还原

【Abstract】 In this paper,the G′/G-expansion method is further extended to construct exact solutions of the(2+1)-dimensional breaking soliton equations.As a result,three types of travelling wave involving parameters are obtained.When the parameters are taken as special values the solitary waves are also derived from the travelling waves.The travelling wave solutions are expressed by the hyperbolic functions,the trigonometric functions and the rational functions.The results show the improved method with the aid a second-order linear ODE provided a very effective and powerful mathematical tool for solving many non-linear PDEs in mathematical physics.更多还原