Integrability classification and explicit solutions to a class of vc-BKdV equations

Hanze Liu; Hanze Liu

doi:10.3934/math.2026701

AIMS Mathematics

2026, Volume 11, Issue 6: 17115-17123. doi: 10.3934/math.2026701

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Integrability classification and explicit solutions to a class of vc-BKdV equations

Hanze Liu ^,

Department of General Education, Shandong Xiehe University, Jinan 250109, China

Received: 26 March 2026 Revised: 05 May 2026 Accepted: 19 May 2026 Published: 12 June 2026
MSC : 37K10, 35C05, 35Q53

The variable-coefficient equations play an important role in mathematical physics and physical applications. However, it is very difficult to study exact solutions and other properties of such equations. In this paper, we investigate the complete integrability classification of a class of the generalized variable-coefficient nonlinear wave equation by the Painlevé method, the integrability and integrable conditions of the variable-coefficient equations are obtained, then the exact solutions are provided by the truncated expansion method. Moreover, some new types of explicit solutions to the nonlinear variable-coefficient equations are investigated by the invariant subspace method (ISM).
- Painlevé method,
- integrability,
- truncated expansion,
- invariant subspace method,
- explicit solution
Citation: Hanze Liu. Integrability classification and explicit solutions to a class of vc-BKdV equations[J]. AIMS Mathematics, 2026, 11(6): 17115-17123. doi: 10.3934/math.2026701

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Abstract

The variable-coefficient equations play an important role in mathematical physics and physical applications. However, it is very difficult to study exact solutions and other properties of such equations. In this paper, we investigate the complete integrability classification of a class of the generalized variable-coefficient nonlinear wave equation by the Painlevé method, the integrability and integrable conditions of the variable-coefficient equations are obtained, then the exact solutions are provided by the truncated expansion method. Moreover, some new types of explicit solutions to the nonlinear variable-coefficient equations are investigated by the invariant subspace method (ISM).

References

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