Special symmetries to standard Riccati equations and applications

DOI10.1016/j.amc.2010.04.039zbMath1202.34007OpenAlexW1995896722MaRDI QIDQ984342

J. Martínez

Publication date: 19 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.04.039

zbMATH Keywords

Lie groupsintegrability conditionRiccati equation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (9)

Solving nonlinear partial differential equations by the sn-ns method ⋮ On a KdV equation with higher-order nonlinearity: Traveling wave solutions ⋮ Computing exact solutions to a generalized Lax-Sawada-Kotera-Itô seventh-order KdV equation ⋮ Closed form solutions for a generalized Benjamin-Bona-Mahony-Burgers equation with higher-order nonlinearity ⋮ Lie symmetries for Lie systems: applications to systems of ODEs and PDEs ⋮ A nonlinear fractional Sharma-Tasso-Olver equation: new exact solutions ⋮ Exact solutions of the fractional Sharma-Tasso-Olver equation and the fractional Bogoyavlenskii's breaking soliton equations ⋮ Closed Form Solutions of the Perturbed GerdjikovIvanov Equation With Variable Coefficients ⋮ Riccati-Ermakov systems and explicit solutions for variable coefficient reaction-diffusion equations

Uses Software

• PDESpecialSolutions

Cites Work

• The Riccati equation with variable coefficients expansion algorithm to find more exact solutions of nonlinear differential equations
• The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
• Computing exact solutions for some fifth KdV equations with forcing term
• The generalized tanh-coth method to special types of the fifth-order KdV equation
• Special forms of the fifth-order KdV equation with new periodic and soliton solutions
• Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs
• A new case of integrability of the general Riccati equation and its application to relaxation problems
• THE NONLINEAR SUPERPOSITION PRINCIPLE AND THE WEI-NORMAN METHOD
• On Solutions of Certain Riccati Differential Equations
• Some Separable Forms of the Riccati Equation
• Methods of Solution of the Riccati Differential Equation
• Symmetries and differential equations
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