Separation of variables for nonlinear equations of hyperbolic and Korteweg-de Vries type

DOI10.1016/S0034-4877(11)60029-3zbMath1241.35173MaRDI QIDQ429235

Ivan I. Yuryk, Anatoliy F. Barannyk, Tatjana A. Barannyk

Publication date: 26 June 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Korteweg-de Vries equationsLie methodnonlinear hyperbolic equationsgeneralized separation of variables

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Second-order nonlinear hyperbolic equations (35L70)

Related Items (7)

Generalized separation of variables for nonlinear equation \(u_{tt} = F(u)u_{xx} + aF'(u)u_x^2\) ⋮ Exact solutions of the nonlinear equation \(u_{tt} = a(t)uu_{xx} + b(t)u_x^2 + c(t)u\) ⋮ Partial solutions of a system of Euler equations ⋮ Application of group-theoretical methods to solving the point explosion problem in incompressible liquid ⋮ Solutions to non-linear Euler-Poisson-Darboux equations by means of generalized separation of variables ⋮ Exact solutions with generalized separation of variables in the nonlinear heat equation ⋮ A method for the construction of exact solutions to the nonlinear heat equation \(u_t = (F(U)U_x)_X + G(U)U_{x} + H(U)\)

Cites Work

• Exact solutions and invariant spaces for nonlinear gradient diffusion equations
• New exact solutions of parabolic equations with quadratic non-linearities
• Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
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