A simple fast method in finding particular solutions of some nonlinear PDE

被引：20

作者：

Liu Shi-kuo

Fu Zun-tao

Liu Shi-da

Zhao Qiang

机构：

[1] Peking University,Department of Geophysics

[2] Peking University,SKLTR

来源：

Applied Mathematics and Mechanics | 2001年 / 22卷 / 3期

关键词：

trial function method; nonlinear PDE; shock wave solution; solitary wave solution; O175; O411;

D O I：

10.1007/BF02437971

中图分类号：

学科分类号：

摘要：

The “trial function method” (TFM for short) and a routine way in finding traveling wave solutions to some nonlinear partial differential equations (PDE for short) wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.

引用

页码：326 / 331

页数：5

共 19 条

[1]

Kuramoto Y(1978)Diffusion-induced chaos in reaction-diffusion systems Prog Theor Phys Suppl 64 346-350

[2]

Burgers J M(1949)A mathematical model illustrating the theory of turbulence Adv Appl Mech 1 171-175

[3]

Shi-da Liu(1992)KdV-Burgers modeling of turbulence Science in China A 35 576-577

[4]

Shi-kuo Liu(1983)Formulation of saturated solutions in a nonlinear dispersive system with instability and dissipation Phys Rev Lett 51 381-387

[5]

Kawahara T(1995)A class of exact, periodic solutions of nonlinear envelope equations J Math Phys 36 4125-4137

[6]

Kwok W(1990)Exact solutions of the generalized Kuramoto-Sivashinsky equation Phys, Lett A 147 287-291

[7]

Chow N A(1996)Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics Phys Lett A 216 67-75

[8]

Kudryashov Wang(1998)Geometric approach for finding exact solutions to nonlinear partial differential equations Phys Lett A 246 105-112

[9]

Ming-liang Zhou(1989)A kind of analytical solutions of Burgers-KdV equation Kexue Tongbao (Chinese Science Bulletin) 34 26-29

[10]

Yu-bin Li(1991)Heteroclinic orbit on the KdV-Burgers equation and Fisher equation Commun Theor Phys 16 497-500

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