Two types of new algorithms for finding explicit analytical solutions of nonlinear differential equations

DOI10.1007/BF02459221zbMath1008.76074OpenAlexW2324046349MaRDI QIDQ5932101

Hong-Qing Zhang, Zhenya Yan

Publication date: 6 May 2001

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02459221

zbMATH Keywords

nonlinear differential equationsBurgers equationtransformationMATHEMATICAapproximate shallow water equationexplicit analytical solutionsMAPLEvariable-coefficient KdV equation

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25)

Uses Software

• Maple
• Mathematica

Cites Work

• Superfluous order and the proper solution of the Maxwell equation
• Constructions of the general solution for a system of partial differential equations with variable coefficients
• Bäcklund transformation and exact solutions for \((2+1)\)-dimensional Kolmogorov-Petrovsky-Piscounov equation
• Explicit and exact solutions for the generalized reaction Duffing equation
• New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics
• Symmetries and differential equations
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