中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120201-120201.doi: 10.1088/1674-1056/acf706
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Feng Yuan(袁丰)1,†, Behzad Ghanbari2, Yongshuai Zhang(张永帅)3, and Abdul Majid Wazwaz4
Feng Yuan(袁丰)1,†, Behzad Ghanbari2, Yongshuai Zhang(张永帅)3, and Abdul Majid Wazwaz4
摘要: Periodic solutions of the Zakharov equation are investigated. By performing the limit operation λ2l-1 to λ1 on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation, an order-n breather-positon solution is first obtained from a plane wave seed. It is then proven that an order-n lump solution can be further constructed by taking the limit λ1 to λ0 on the breather-positon solution, because the unique eigenvalue λ0 associated with the Lax pair eigenfunction Ψ(λ0)=0 corresponds to the limit of the infinite-periodic solutions. A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.
中图分类号: (Integrable systems)