Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems

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Atıf İçin Kopyala

Sheftel M. B., Yazici D.

Communications in Nonlinear Science and Numerical Simulation, cilt.112, 2022 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 112
• Basım Tarihi: 2022
• Doi Numarası: 10.1016/j.cnsns.2022.106527
• Dergi Adı: Communications in Nonlinear Science and Numerical Simulation
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
• Anahtar Kelimeler: Lax pair, Recursion operator, Skew factorization, Bi-Hamiltonian system
• Yıldız Teknik Üniversitesi Adresli: Evet

Özet

© 2022 Elsevier B.V.We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler–Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component forms and find Hamiltonian representations of all these systems using Dirac's theory of constraints. We consider three-parameter integrable equations that are cubic in partial derivatives of the unknown applying our method of skew factorization of the symmetry condition. Lax pairs and recursion relations for symmetries are determined both for one-component and two-component forms. For cubic three-parameter equations in the two-component form we obtain recursion operators in 2 × 2 matrix form and bi-Hamiltonian representations, thus discovering three new bi-Hamiltonian (2+1) systems.