Classical Darboux transformation and exact soliton solutions of a two-component complex short pulse equation
This paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023442?viewType=HTML |
| Summary: | This paper investigates soliton solutions to a two-component complex short pulse (c-SP) equation. Based on the known Lax pair representation of this equation, we verify the integrability of a two-component c-SP equation and find an equivalent convenient Lax pair through hodograph transformation. The classical Darboux transformation (DT) is utilized to construct multi-soliton solutions for the two-component c-SP equation as an ordinary determinant. Furthermore, the details of one-soliton and two-soliton solutions are presented and generalized for N-fold soliton solutions. We also derive exact soliton solutions in explicit form using suitable reduction constraints from various "seed" solutions and explore them via graphs. |
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| ISSN: | 2473-6988 |