A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem
The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explici...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/6/927 |
| _version_ | 1797240137689595904 |
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| author | Wen-Xiu Ma |
| author_facet | Wen-Xiu Ma |
| author_sort | Wen-Xiu Ma |
| collection | DOAJ |
| description | The aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters. |
| first_indexed | 2024-04-24T18:02:39Z |
| format | Article |
| id | doaj.art-750b8a5b71a845f484afda51639dfdba |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:39Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-750b8a5b71a845f484afda51639dfdba2024-03-27T13:53:20ZengMDPI AGMathematics2227-73902024-03-0112692710.3390/math12060927A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral ProblemWen-Xiu Ma0Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaThe aim of this paper is to analyze a specific fourth-order matrix spectral problem involving four potentials and two free nonzero parameters and construct an associated integrable hierarchy of bi-Hamiltonian equations within the zero curvature formulation. A hereditary recursion operator is explicitly computed, and the corresponding bi-Hamiltonian formulation is established by the so-called trace identity, showing the Liouville integrability of the obtained hierarchy. Two illustrative examples are novel generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations with four components and two adjustable parameters.https://www.mdpi.com/2227-7390/12/6/927matrix spectral problemLax pairintegrable hierarchymonlinear Schrödinger equationsmodified Korteweg–de Vries equations |
| spellingShingle | Wen-Xiu Ma A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem Mathematics matrix spectral problem Lax pair integrable hierarchy monlinear Schrödinger equations modified Korteweg–de Vries equations |
| title | A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem |
| title_full | A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem |
| title_fullStr | A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem |
| title_full_unstemmed | A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem |
| title_short | A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem |
| title_sort | generalized hierarchy of combined integrable bi hamiltonian equations from a specific fourth order matrix spectral problem |
| topic | matrix spectral problem Lax pair integrable hierarchy monlinear Schrödinger equations modified Korteweg–de Vries equations |
| url | https://www.mdpi.com/2227-7390/12/6/927 |
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