High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation
A series of new soliton solutions is presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann–Hilbert method and transformation relationship. Firstly, through a standard dressing procedure, the N-soliton matrix associated with the simple zeros in the Riemann–Hilbert...
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| Published in | Communications in nonlinear science & numerical simulation Vol. 120; p. 107149 |
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| Format | Journal Article |
| Language | English |
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01.06.2023
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| Abstract | A series of new soliton solutions is presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann–Hilbert method and transformation relationship. Firstly, through a standard dressing procedure, the N-soliton matrix associated with the simple zeros in the Riemann–Hilbert problem for the Hirota equation is constructed. Then the N-soliton matrix of the inhomogeneous variable coefficient Hirota equation can be obtained by a special relationship transformation from the N-soliton matrix of the Hirota equation. Next, using the generalized Darboux transformation, the high-order soliton solutions corresponding to the elementary high-order zeros in the Riemann–Hilbert problem for the Hirota equation can be derived. Similarly, employing the relationship transformation mentioned above can lead to the high-order soliton solutions of the inhomogeneous variable coefficient Hirota equation. In addition, the collision dynamics of Hirota and inhomogeneous variable coefficient Hirota equations are analyzed; the asymptotic behaviors for multi-solitons and long-term asymptotic estimates for the high-order one-soliton of the Hirota equation are concretely calculated. Most notably, by analyzing the dynamics of the multi-solitons and high-order solitons of the inhomogeneous variable coefficient Hirota equation, we discover numerous new waveforms such as heart-shaped periodic wave solutions, O-shaped periodic wave solutions etc. that have never been reported before, which are crucial in theory and practice.
•Construct high-order soliton solutions for the variable coefficient Hirota equation.•Construct solutions of the Hirota equation by the Riemann-Hilbert method.•Obtain solutions of variable coefficient equation by relationship transformation.•Collision dynamics, asymptotic behaviors and long-term asymptotic are analyzed.•Discover numerous new waveforms that have never been reported before. |
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| AbstractList | A series of new soliton solutions is presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann–Hilbert method and transformation relationship. Firstly, through a standard dressing procedure, the N-soliton matrix associated with the simple zeros in the Riemann–Hilbert problem for the Hirota equation is constructed. Then the N-soliton matrix of the inhomogeneous variable coefficient Hirota equation can be obtained by a special relationship transformation from the N-soliton matrix of the Hirota equation. Next, using the generalized Darboux transformation, the high-order soliton solutions corresponding to the elementary high-order zeros in the Riemann–Hilbert problem for the Hirota equation can be derived. Similarly, employing the relationship transformation mentioned above can lead to the high-order soliton solutions of the inhomogeneous variable coefficient Hirota equation. In addition, the collision dynamics of Hirota and inhomogeneous variable coefficient Hirota equations are analyzed; the asymptotic behaviors for multi-solitons and long-term asymptotic estimates for the high-order one-soliton of the Hirota equation are concretely calculated. Most notably, by analyzing the dynamics of the multi-solitons and high-order solitons of the inhomogeneous variable coefficient Hirota equation, we discover numerous new waveforms such as heart-shaped periodic wave solutions, O-shaped periodic wave solutions etc. that have never been reported before, which are crucial in theory and practice.
•Construct high-order soliton solutions for the variable coefficient Hirota equation.•Construct solutions of the Hirota equation by the Riemann-Hilbert method.•Obtain solutions of variable coefficient equation by relationship transformation.•Collision dynamics, asymptotic behaviors and long-term asymptotic are analyzed.•Discover numerous new waveforms that have never been reported before. |
| ArticleNumber | 107149 |
| Author | Zhou, Hui-Juan Chen, Yong |
| Author_xml | – sequence: 1 givenname: Hui-Juan surname: Zhou fullname: Zhou, Hui-Juan organization: School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, China – sequence: 2 givenname: Yong surname: Chen fullname: Chen, Yong email: ychen@sei.ecnu.edu.cn organization: School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, China |
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| Keywords | Relationship transformation High-order soliton Inhomogeneous variable coefficient Hirota equation Riemann–Hilbert problem |
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| Snippet | A series of new soliton solutions is presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann–Hilbert method and... |
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| SubjectTerms | High-order soliton Inhomogeneous variable coefficient Hirota equation Relationship transformation Riemann–Hilbert problem |
| Title | High-order soliton solutions and their dynamics in the inhomogeneous variable coefficients Hirota equation |
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