CAJ | 학술논문

物理学方程，尤其是在流体力学、空气动力学、等离子体物理、生物物理和化学物理等现代科学技术中引出的非线性发展方程，其精确解有重大的理论和应用研究价值，许多数学家和物理学家为此作了大量工作．借助于符号计算软件Maple，通过利用一个新的更为广义的Ric—cati方程有理展开法，得到了非线性项具有任意次幂的非线性反应扩散方程的一些新的更广义的精确解．此方法还可以应用到其他的非线性发展方程中去．
물이학방정，우기시재류체역학、공기동역학、등리자체물리、생물물리화화학물리등현대과학기술중인출적비선성발전방정，기정학해유중대적이론화응용연구개치，허다수학가화물이학가위차작료대량공작．차조우부호계산연건Maple，통과이용일개신적경위엄의적Ric—cati방정유리전개법，득도료비선성항구유임의차멱적비선성반응확산방정적일사신적경엄의적정학해．차방법환가이응용도기타적비선성발전방정중거．
Many nonlinear evolution equations were arisen form physics equations, especially in the fluid me- chanics, aerodynamics, plasma physics, biology physical and chemical physical, etc. Because the precise so- lution is of great theoretical and applied research value, many mathematicians and physicists did a lot of work. In this paper, based upon a new generalized Projective Riccati equation rational expansion method, some new generalexact solutions are obtained for the single-nonlinear reaction-diffusion equation with nonlinear terms of arbitrary order. The presented method can also be applied to other nonlinear evolution equations with nonlinear terms of arbitrary order.