Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915954891423744 |
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| author | Samokhin, Alexey |
| author_facet | Samokhin, Alexey |
| contents | Spherical and cylindrical KdV-B equations have few known exact solutions, yet these solutions are hard to be interpreted physically. But these equations do have a family of diverging shock waves. Their properties such as
asymptotic modes, stability, rules of their interactions/superposition are the subject of this paper. It gives a detailed asymptotic description of the one-parameter families of shock wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable to a wide class of shock waves, in particular discontinuous. Typical examples are illustrated by graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_22389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition Samokhin, Alexey Pattern Formation and Solitons 35Q53, 35B36 Spherical and cylindrical KdV-B equations have few known exact solutions, yet these solutions are hard to be interpreted physically. But these equations do have a family of diverging shock waves. Their properties such as asymptotic modes, stability, rules of their interactions/superposition are the subject of this paper. It gives a detailed asymptotic description of the one-parameter families of shock wave solutions and proves their stability using a conservation law. Based on these results, effective rules of superposition are obtained. Moreover these rules are applicable to a wide class of shock waves, in particular discontinuous. Typical examples are illustrated by graphs. |
| title | Shock waves of spherical/cylindrical KdV-B: Asymptotic, stability, superposition |
| topic | Pattern Formation and Solitons 35Q53, 35B36 |
| url | https://arxiv.org/abs/2604.22389 |