Lump waves in a generalized Bogoyavlensky-Konopelchenko model with spatially balanced derivatives

Wen-Xiu Ma; Wen-Xiu Ma

doi:10.3934/mine.2026005

Mathematics in Engineering

2026, Volume 8, Issue 1: 140-149. doi: 10.3934/mine.2026005

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Research article

Lump waves in a generalized Bogoyavlensky-Konopelchenko model with spatially balanced derivatives

Wen-Xiu Ma ^{1,2,3,4
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1.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2.
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, Baku 1096, Azerbaijan
3.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
4.
Material Science Innovation and Modelling, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received: 12 October 2025 Accepted: 04 February 2026 Published: 10 February 2026

This paper investigates lump waves in a generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko model with spatially balanced derivatives. Using a sum-of-squares ansatz, symbolic computation in Maple is employed to construct lump wave solutions of the nonlinear model from positive quadratic functions. The interplay of four sets of nonlinear terms and five dispersion terms gives rise to the resulting lump waves. The critical points of these quadratic functions are determined, and they travel at constant velocities along a straight line in the spatial plane. Along this characteristic line, the constructed lump waves remain invariant. Concluding remarks are provided in the final section.
- lump wave,
- Hirota bilinear form,
- soliton,
- symbolic computation,
- nonlinearity,
- dispersion
Citation: Wen-Xiu Ma. Lump waves in a generalized Bogoyavlensky-Konopelchenko model with spatially balanced derivatives[J]. Mathematics in Engineering, 2026, 8(1): 140-149. doi: 10.3934/mine.2026005

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Abstract

This paper investigates lump waves in a generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko model with spatially balanced derivatives. Using a sum-of-squares ansatz, symbolic computation in Maple is employed to construct lump wave solutions of the nonlinear model from positive quadratic functions. The interplay of four sets of nonlinear terms and five dispersion terms gives rise to the resulting lump waves. The critical points of these quadratic functions are determined, and they travel at constant velocities along a straight line in the spatial plane. Along this characteristic line, the constructed lump waves remain invariant. Concluding remarks are provided in the final section.

References

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