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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 4: Continuous and Discrete Integrable Systems with Applications
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Original Articles

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

Douglas Poole Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401-1887, USA
&
Willy Hereman Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, CO 80401-1887, USACorrespondence[email protected]
Pages 433-455 | Received 26 Jul 2009, Published online: 12 Feb 2010

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S. Reza Hejazi & Shaban Mohammadi. (2024) Lie symmetry, numerical solution with spectral method and conservation laws of Degasperis–Procesi equation by homotopy and direct methods. International Journal of Modelling and Simulation 44:2, pages 61-76.
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AH Kara. (2021) On the invariance and conservation laws of differential equations. Transactions of the Royal Society of South Africa 76:1, pages 89-95.
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Articles from other publishers (23)

P. E. Hydon. (2023) Partial Euler operators and the efficient inversion of Div. European Journal of Applied Mathematics 34:5, pages 1046-1066.
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Jaskiran Kaur, Manjit Singh & Mukesh. (2023) Infinite Dimensional Symmetry Group Reductions and Conservation Laws of Lin–Reissner–Tsien Equation. International Journal of Applied and Computational Mathematics 9:5.
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Manjit Singh & Shou-Fu Tian. (2022) Lie symmetries, group classification and conserved quantities of dispersionless Manakov–Santini system in (2+1)-dimension. Indian Journal of Pure and Applied Mathematics 54:2, pages 312-329.
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Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas & Olivier Verdier. (2023) The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators. Forum of Mathematics, Sigma 11.
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Gangwei Wang, Li Li & A H Kara. (2022) Consistent Burgers equation expansion method and its applications to high dimensional Burgers-type equations. Communications in Theoretical Physics.
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Anjan Biswas, Abdul H. Kara, Qin Zhou, Abdullah Kamis Alzahrani & Milivoj R. Belic. (2020) Conservation Laws for Highly Dispersive Optical Solitons in Birefringent Fibers. Regular and Chaotic Dynamics 25:2, pages 166-177.
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J. R. Espinosa. (2019) Fresh look at the calculation of tunneling actions including gravitational effects. Physical Review D 100:10.
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Manjit Singh & R K Gupta. (2018) Group classification, conservation laws and Painlevé analysis for Klein–Gordon–Zakharov equations in (3 $$+$$ + 1)-dimension. Pramana 92:1.
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A. H. Kara. (2018) On the Relationship between the Invariance and Conservation Laws of Differential Equations. Journal of Mathematics 2018, pages 1-5.
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Manjit Singh & R. K. Gupta. (2018) On Painlevé Analysis, Symmetry Group and Conservation Laws of Date–Jimbo–Kashiwara–Miwa Equation. International Journal of Applied and Computational Mathematics 4:3.
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STEPHEN C. ANCO & ABDUL H. KARA. (2017) Symmetry-invariant conservation laws of partial differential equations. European Journal of Applied Mathematics 29:1, pages 78-117.
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Stephen C. Anco & Chaudry Masood Khalique. (2016) Conservation laws of coupled semilinear wave equations. International Journal of Modern Physics B 30:28n29, pages 1640004.
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Stephen C. Anco. (2016) Symmetry properties of conservation laws. International Journal of Modern Physics B 30:28n29, pages 1640003.
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S C Anco, E D Avdonina, A Gainetdinova, L R Galiakberova, N H Ibragimov & T Wolf. (2016) Symmetries and conservation laws of the generalized Krichever–Novikov equation. Journal of Physics A: Mathematical and Theoretical 49:10, pages 105201.
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Maryam Khorshidi, Mehdi Nadjafikhah, Hossein Jafari & Maysaa Al Qurashi. (2016) Reductions and conservation laws for BBM and modified BBM equations. Open Mathematics 14:1, pages 1138-1148.
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Zhonglong Zhao & Bo Han. (2015) On optimal system, exact solutions and conservation laws of the Broer-Kaup system. The European Physical Journal Plus 130:11.
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Stephen C. Anco, Priscila Leal da Silva & Igor Leite Freire. (2015) A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations. Journal of Mathematical Physics 56:9.
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Reza Dastranj & Mehdi Nadjafikhah. (2014) Symmetry analysis and conservation laws for description of waves in bubbly liquid. International Journal of Non-Linear Mechanics 67, pages 48-51.
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Vahid Shirvani-Sh & Mehdi Nadjafikhah. (2014) Conservation laws and exact solutions of the Whitham-type equations. Communications in Nonlinear Science and Numerical Simulation 19:7, pages 2212-2219.
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Mehdi Nadjafikhah & Mostafa Hesamiarshad. (2014) Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation. Abstract and Applied Analysis 2014, pages 1-7.
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Mehdi Nadjafikhah & Fatemeh Ahangari. (2013) Symmetry Analysis and Conservation Laws for the Hunter—Saxton Equation. Communications in Theoretical Physics 59:3, pages 335-348.
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Mehdi Nadjafikhah & Vahid Shirvani-Sh. (2012) Lie symmetries and conservation laws of the Hirota–Ramani equation. Communications in Nonlinear Science and Numerical Simulation 17:11, pages 4064-4073.
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Douglas Poole & Willy Hereman. (2011) Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions. Journal of Symbolic Computation 46:12, pages 1355-1377.
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