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arXiv · 2512.14159

Integrable variant Blaszak-Szum lattice equation

Wei-Kang Xie·Guo-Fu Yu
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Abstract

We derive a novel variant of the Blaszak-Szum lattice equation by introducing a new class of trigonometric-type bilinear operators. By employing Hirota's bilinear method, we obtain the Gram-type determinant solution of the variant Blaszak-Szum lattice equation. One-soliton and two-soliton solutions are constructed, with a detailed analysis of the asymptotic behaviors of the two-soliton solution. A B\"acklund transformation for the variant Blaszak-Szum lattice equation is established. By virtue of this B\"acklund transformation, multi-lump solutions of the equation are further constructed. Rational solutions are derived by introducing two differential operators applied to the determinant elements; in particular, lump solutions derived via these differential operators can be formulated in terms of Schur polynomials. Through parameter variation, three types of breather solutions are obtained, including the Akhmediev breather, Kuznetsov-Ma breather, and a general breather that propagates along arbitrary oblique trajectories. Finally, numerical three-periodic wave solutions to the variant Blaszak-Szum lattice equation are computed using the Gauss-Newton method.

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Wei-Kang Xie, Guo-Fu Yu. 2025-12-16. Integrable variant Blaszak-Szum lattice equation. https://arxiv.org/abs/2512.14159

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