An <i>n</i>-order expansion method for determining the upper bound of the order of finite series solutions

SONG Chenwei; LIU Yinping

doi:10.3969/j.issn.1000-5641.2021.03.007

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SONG Chenwei, LIU Yinping. An n-order expansion method for determining the upper bound of the order of finite series solutions[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007

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SONG Chenwei, LIU Yinping. An n-order expansion method for determining the upper bound of the order of finite series solutions[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 56-64. doi: 10.3969/j.issn.1000-5641.2021.03.007

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An n-order expansion method for determining the upper bound of the order of finite series solutions

doi: 10.3969/j.issn.1000-5641.2021.03.007

SONG Chenwei¹,
LIU Yinping^{2
,
,}

1.
School of Computer Science and Technology, East China Normal University, Shanghai　200062, China
2.
School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received Date: 2020-03-12
Publish Date: 2021-05-01

Abstract

Abstract

A number of algebraic methods used for constructing exact finite series solutions of nonlinear evolution equations are based on the homogeneous balance principle, such as the tanh function method, the Jacobi elliptic function method, the Painlevé truncated expansion method, the CRE method, etc. In each of these methods, the order of required solutions is determined by the homogeneous balance principle. In this paper, the homogeneous balance principle is further extended by considering additional balance possibilities. An n-order expansion method is proposed to determine possible new orders of required solutions. By applying the proposed method to several examples, we show that higher orders and new solutions can be obtained.
- nonlinear evolution equation,
- homogeneous balance principle,
- n-order expansion method,
- finite series solution

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References(24)

References

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