Two new reductions methods for polynomial differential equations and applications to nonlinear pdes

DOI10.1016/j.cam.2017.10.025zbMath1387.34057OpenAlexW2768315039MaRDI QIDQ679570

Juan-Miguel Gracia

Publication date: 11 January 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.10.025

zbMATH Keywords

polynomial ordinary differential equationsexact solutions for partial differential equations in mathematical physicsfirst-order reductions

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05) Traveling wave solutions (35C07)

Related Items (1)

A new method to obtain either first- or second-order reductions for parametric polynomial ODEs

Uses Software

• Maple
• PDESpecialSolutions
• Exterior

Cites Work

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• The extended mapping method and its applications for nonlinear evolution equations
• Large cells in nonlinear Marangoni convection
• Symbolic computations of conserved densities for systems of nonlinear evolution equations
• Reductions of PDEs to second order ODEs and symbolic computation
• Reductions of PDEs to first order ODEs, symmetries and symbolic computation
• New exact Jacobi elliptic function solutions for some nonlinear evolution equations
• Simplest equation method to look for exact solutions of nonlinear differential equations
• Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
• New methods of reduction for ordinary differential equations
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Scaling invariant Lax pairs of nonlinear evolution equations
• On the Benney equation
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Chaotic Pulse Trains
• Hidden symmetries and nonlocal group generators for ordinary differential equations
• Integrals of nonlinear equations of evolution and solitary waves
• Some Properties of Long Nonlinear Waves

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