Two types of elliptic dark soliton solutions for the Hirota equation

2025/04/09 by Qiaofeng Huang, Xuan Sun, Huang, Qiaofeng +1 · 1 voice · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Partial Differential Equations #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.2504.06871

Abstract

We primarily study concave-downward and convex-upward types of elliptic dark soliton solutions for the Hirota equation, exhibiting a concave-downward shape on both upper and lower envelope surfaces and showing a convex-upward shape on the lower envelope surface, respectively. By analyzing the supremum and infimum of solutions, we provide the existence conditions for these two types of elliptic dark solitons. Additionally, we study two-elliptic dark soliton solutions combining both types with the same velocity and investigate the elastic collisions between these two types of solutions with different velocities.

Citations

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Cited by

• Bright and dark breathers on an elliptic wave in the defocusing mKdV equation

Discussions

• Qiaofeng Huang, Xuan Sun: Two types of elliptic dark soliton solutions for the Hirota equation https://arxiv.org/abs/2504.06871 https://arxiv.org/pdf/2504.06871 https://arxiv.org/html/2504.06871 [bsky, 0 points, 1 comments]

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