The parametrically extended Kardar-Parisi-Zhang equation, its dark-type generalization, and integrability

DOI10.1007/978-3-031-30284-8_21MaRDI QIDQ6606763

Anatoliy K. Prykarpatsky, Myroslava I. Kopych, P. Ya. Pukach

Publication date: 17 September 2024

zbMATH Keywords

conservation lawsintegrabilitypartial differential equationsKardar-Parisi-Zhang equation

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear ordinary differential equations and systems (34A34) Invariance and symmetry properties for PDEs on manifolds (58J70) Initial value problems for nonlinear higher-order PDEs (35G25) Applications of Lie algebras and superalgebras to integrable systems (17B80) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Overdetermined systems of PDEs with variable coefficients (35N10) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Cites Work

• Integrability analysis of a two-component Burgers-type hierarchy
• Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type
• Complete integrability of the nonlinear Itô and Benney-Kaup systems: Gradient algorithm and Lax representation
• Mathematics of dispersive water waves
• Dark Equations
• Dynamic Scaling of Growing Interfaces
• Invitation to Partial Differential Equations
• Floquet theory for partial differential equations
• Quasi-linearization and stability analysis of some self-dual, dark equations and a new dynamical system ^†
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