The homotopy operator method for symbolic integration by parts and inversion of divergences with applications

DOI10.1080/00036810903208155zbMath1193.37077arXiv0908.0399OpenAlexW1970278661WikidataQ58188772 ScholiaQ58188772MaRDI QIDQ3558501

Douglas Poole, Willy Hereman

Publication date: 5 May 2010

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.0399

zbMATH Keywords

conservation lawcomplete integrabilityhomotopy operatortotal divergenceEuler operatorexact differential function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Nonlinear evolution equations (47J35)

Related Items (16)

Unnamed Item ⋮ A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations ⋮ Symmetry-invariant conservation laws of partial differential equations ⋮ Consistent Burgers equation expansion method and its applications to high- dimensional Burgers-type equations ⋮ Partial Euler operators and the efficient inversion of Div ⋮ Lie symmetries, group classification and conserved quantities of dispersionless Manakov-Santini system in \((2+1)\)-dimension ⋮ The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators ⋮ Lie symmetries and conservation laws of the Hirota-Ramani equation ⋮ Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions ⋮ Analysis of the symmetries and conservation laws of the nonlinear Jaulent-Miodek equation ⋮ On the relationship between the invariance and conservation laws of differential equations ⋮ Reductions and conservation laws for BBM and modified BBM equations ⋮ Conservation laws for highly dispersive optical solitons in birefringent fibers ⋮ Unnamed Item ⋮ On Painlevé analysis, symmetry group and conservation laws of Date-Jimbo-Kashiwara-Miwa equation ⋮ Conservation laws and exact solutions of the Whitham-type equations

Uses Software

• Maple
• Mathematica
• REDUCE

Cites Work

• GeM software package for computation of symmetries and conservation laws of differential equations
• Continuous and discrete homotopy operators: a theoretical approach made concrete
• Symbolic computations of conserved densities for systems of nonlinear evolution equations
• Differential forms. With applications to the physical sciences
• Symbolic computation of conservation laws of nonlinear partial differential equations in multi‐dimensions
• Analytic aspects of the Zakharov–Kuznetsov equation
• Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws

This page was built for publication: The homotopy operator method for symbolic integration by parts and inversion of divergences with applications